id int64 | problem_number string | title string | statement string | background string | difficulty_level_id int64 | status string | proposed_by string | proposed_year int64 | category_id int64 | set_id int64 | view_count int64 | favorite_count int64 | created_at timestamp[s] | updated_at timestamp[s] | published bool | category dict | difficulty dict | set dict | duplicates list | status_review unknown | archive_reason string | duplicate_of list | old_problem_number string | notes string | tags list | literature_assessment string | literature_sources list | literature_checked_at timestamp[s] | solution_reference string | source_url string | source string | prize string | references list | clean_statement string | original_statement string | statement_status string | statement_verification string | research_classification string | research_summary string | research_difficulty_suggested string | historical_research_summary string | research_summary_reviewed_at timestamp[s] | source_citation string |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
30,003,216 | OWR-14750-001 | Convergence of Adaptive Hybrid Finite Element Methods | Does the adaptive hybrid finite-element procedure driven by the two-step a posteriori flux-error estimator converge? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Self-Adaptive Numerical Methods for Computationally Challenging Problems (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/42, pp. 2399--2464](https://doi.org/10.4171/owr/2016/42)
## Liter... | 3 | open | null | 2,016 | 9 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 9,
"name": "pde",
"display_name": "Partial Differential Equations",
"description": "PDEs and their applications in physics and geometry.",
"slug": "pde",
"order_index": 9,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14750-001",
"literature-status:open",
"owr-year:2016"
] | For the hybrid two-step finite-element flux estimator, reliability and efficiency are known, but convergence of the adaptive procedure driven by this estimator was explicitly left open and no general proof was located. | [
{
"url": "https://doi.org/10.4171/owr/2016/42",
"label": "original open problem"
},
{
"url": "https://doi.org/10.1016/S0377-0427(23)00615-5",
"label": "later hybrid estimator work"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/42 | null | null | null | Does the adaptive hybrid finite-element procedure driven by the two-step a posteriori flux-error estimator converge? | Does the adaptive procedure based on the proposed a posteriori error estimator for the hybrid finite element method converge? | corrected_verified | The official report passage was checked and the statement was rewritten as a self-contained problem while preserving its mathematical content. | null | null | null | null | null | Self-Adaptive Numerical Methods for Computationally Challenging Problems (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/42, pp. 2399--2464 |
30,003,217 | OWR-14751-001 | Zero-Velocity Lieb–Robinson Bounds for Disordered Spin Systems | Can zero-velocity Lieb–Robinson bounds be proved for general disordered finite-range quantum spin models on $\mathbb Z^d$, thereby establishing a universal many-body-localized phase? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Many-Body Quantum Systems and Effective Theories (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/43, pp. 2465--2511](https://doi.org/10.4171/owr/2016/43)
## Literature review (checked 20... | 3 | open | null | 2,016 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14751-001",
"literature-status:open",
"owr-year:2016"
] | Zero-velocity Lieb--Robinson bounds are proved for several localized or one-dimensional disordered models, but a theorem for general disordered finite-range spin systems on arbitrary Zd remains open. | [
{
"url": "https://doi.org/10.4171/owr/2016/43",
"label": "original open problem"
},
{
"url": "https://arxiv.org/abs/1108.3811",
"label": "Hamza--Sims--Stolz"
},
{
"url": "https://doi.org/10.1103/PRXQuantum.4.020349",
"label": "one-dimensional disordered bounds"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/43 | null | null | null | Can zero-velocity Lieb–Robinson bounds be proved for general disordered finite-range quantum spin models on $\mathbb Z^d$, thereby establishing a universal many-body-localized phase? | Can zero-velocity Lieb--Robinson bounds be proved for general disordered finite-range quantum spin models on \mathbb Z^d, thereby establishing a universal many-body-localized phase? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Many-Body Quantum Systems and Effective Theories (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/43, pp. 2465--2511 |
30,003,218 | OWR-14751-002 | Sharp Spectral-Cluster Density Bounds on Manifolds | Let $M$ be smooth, compact, and boundaryless, let $E_\lambda=\mathbf{1}_{\{x:\lambda^2\leq x<(\lambda+1)^2\}}(\Delta_g)L^2(M)$, and suppose $1\ll r_\lambda\ll\dim E_\lambda$. For $2\leq p\leq\infty$, do there exist subspaces $Q_\lambda\subset E_\lambda$ with $\dim Q_\lambda\sim r_\lambda$ such that $\lVert\rho_{Q_\lamb... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Many-Body Quantum Systems and Effective Theories (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/43, pp. 2465--2511](https://doi.org/10.4171/owr/2016/43)
## Literature review (checked 20... | 3 | open | null | 2,016 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14751-002",
"literature-status:open",
"owr-year:2016"
] | The required subspaces are constructed for the two-sphere, while the exact general-manifold construction in the extracted spectral-cluster problem remains open. | [
{
"url": "https://doi.org/10.4171/owr/2016/43",
"label": "original open problem"
},
{
"url": "https://arxiv.org/abs/1608.08299",
"label": "Frank--Sabin spectral cluster bounds"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/43 | null | null | null | Let $M$ be smooth, compact, and boundaryless, let $E_\lambda=\mathbf{1}_{\{x:\lambda^2\leq x<(\lambda+1)^2\}}(\Delta_g)L^2(M)$, and suppose $1\ll r_\lambda\ll\dim E_\lambda$. For $2\leq p\leq\infty$, do there exist subspaces $Q_\lambda\subset E_\lambda$ with $\dim Q_\lambda\sim r_\lambda$ such that $\lVert\rho_{Q_\lamb... | Let M be smooth, compact, and boundaryless, E_\lambda=\mathbf 1_{[\lambda^2,(\lambda+1)^2)}(\Delta_g)L^2(M), and 1\ll r_\lambda\ll\dim E_\lambda. For 2\le p\le\infty, do there exist Q_\lambda\subset E_\lambda with \dim Q_\lambda\sim r_\lambda such that \|\rho_{Q_\lambda}\|_{L^{p/2}(M)}\ge c\lambda^{2s(p)}r_\lambda^{1/\... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Many-Body Quantum Systems and Effective Theories (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/43, pp. 2465--2511 |
30,003,219 | OWR-14751-003 | Reconstruction of Many-Body Dynamics from One-Particle Density | For time-dependent $N$-boson or $N$-fermion systems with known interactions and initial state, can the full quantum dynamics, and in particular the external potential, be reconstructed from the one-particle density? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Many-Body Quantum Systems and Effective Theories (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/43, pp. 2465--2511](https://doi.org/10.4171/owr/2016/43)
## Literature review (checked 20... | 3 | partially_solved | null | 2,016 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14751-003",
"literature-status:partially-solved",
"owr-year:2016"
] | Runge--Gross theory gives a density--potential and hence density--observable correspondence for a fixed initial state under regularity and representability assumptions, but density alone without those data does not determine arbitrary quantum dynamics. | [
{
"url": "https://doi.org/10.1103/PhysRevLett.52.997",
"label": "Runge--Gross"
},
{
"url": "https://arxiv.org/abs/1610.05552",
"label": "density--potential mapping"
},
{
"url": "https://doi.org/10.1039/D4CP04551C",
"label": "TDDFT foundations review"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/43 | null | null | null | For time-dependent $N$-boson or $N$-fermion systems with known interactions and initial state, can the full quantum dynamics, and in particular the external potential, be reconstructed from the one-particle density? | For time-dependent N-boson or N-fermion systems with known interactions and initial state, can the full quantum dynamics, in particular the external potential, be reconstructed from the one-particle density? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Many-Body Quantum Systems and Effective Theories (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/43, pp. 2465--2511 |
30,003,220 | OWR-14751-004 | Universal Bounds on Atomic Excess Charge | Does there exist a universal constant $C$ such that a nucleus of charge $Z$ can bind at most $Z+C$ electrons in the full many-body Schrödinger theory? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Many-Body Quantum Systems and Effective Theories (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/43, pp. 2465--2511](https://doi.org/10.4171/owr/2016/43)
## Literature review (checked 20... | 3 | open | null | 2,016 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14751-004",
"literature-status:open",
"owr-year:2016"
] | Rigorous results give bounds on excess charge and prove the conjecture in several reduced theories, but the full many-electron quantum statement that a neutral atom binds at most one or two extra electrons remains open. | [
{
"url": "https://doi.org/10.4171/owr/2016/43",
"label": "original open problem"
},
{
"url": "https://arxiv.org/abs/1209.3642",
"label": "Nam review of ionization"
},
{
"url": "https://arxiv.org/abs/2504.18487",
"label": "recent excess-charge bounds"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/43 | null | null | null | Does there exist a universal constant $C$ such that a nucleus of charge $Z$ can bind at most $Z+C$ electrons in the full many-body Schrödinger theory? | Does there exist a universal constant C such that a nucleus of charge Z can bind at most Z+C electrons in the full many-body Schrödinger theory? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Many-Body Quantum Systems and Effective Theories (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/43, pp. 2465--2511 |
30,003,221 | OWR-14751-005 | Ball-Shaped Minimizers of Competing Nonlocal Energies | For
$$
E_\alpha(m)=\inf\left\{E_\alpha[\rho]:0\leq\rho\leq1,\ \int_{\mathbb R^3}\rho=m\right\},
$$
where
$$
E_\alpha[\rho]=\frac12\iint_{\mathbb R^3\times\mathbb R^3}\rho(x)\left(|x-y|^{-1}+|x-y|^\alpha\right)\rho(y)\,dx\,dy,
$$
does there exist $m'_{c_2}(\alpha)<\infty$ such that, whenever $m>m'_{c_2}(\alpha)$, every ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Many-Body Quantum Systems and Effective Theories (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/43, pp. 2465--2511](https://doi.org/10.4171/owr/2016/43)
## Literature review (checked 20... | 3 | solved | null | 2,016 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.2422/2036-2145.201909_007",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes)**. R. L. Frank (joint with E. H. Lieb; OWR 43/2016, p. 2506) asks whether, for E\_α[ρ] = ½∬ρ(x)(|x − y|⁻¹ + |x − y|^α)ρ(y) dx dy on R³ with 0 ≤ ρ ≤ 1 and ∫ρ = m, every minimizer of sufficiently large mass is the characteristic function of a ball. Yes, for eve... | [
"owr",
"oberwolfach-reports",
"OWR-14751-005",
"literature-status:open",
"owr-year:2016"
] | Large-mass minimizers for related nonlocal isoperimetric energies are known to be close to balls, but the exact assertion that every sufficiently large minimizer for the stated kernel is a ball has not been established in the extracted generality. | [
{
"url": "https://doi.org/10.4171/owr/2016/43",
"label": "original open problem"
},
{
"url": "https://www.sciencedirect.com/science/article/abs/pii/S0362546X21000961",
"label": "large-mass minimizers"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/43 | null | null | null | For
$$
E_\alpha(m)=\inf\left\{E_\alpha[\rho]:0\leq\rho\leq1,\ \int_{\mathbb R^3}\rho=m\right\},
$$
where
$$
E_\alpha[\rho]=\frac12\iint_{\mathbb R^3\times\mathbb R^3}\rho(x)\left(|x-y|^{-1}+|x-y|^\alpha\right)\rho(y)\,dx\,dy,
$$
does there exist $m'_{c_2}(\alpha)<\infty$ such that, whenever $m>m'_{c_2}(\alpha)$, every ... | For E_\alpha(m)=\inf\{E_\alpha[\rho]:0\le\rho\le1,\int_{\mathbb R^3}\rho=m\}, with E_\alpha[\rho]=\frac12\iint\rho(x)(|x-y|^{-1}+|x-y|^\alpha)\rho(y) dx dy, does there exist m'_{c_2}(\alpha)<\infty such that for m>m'_{c_2}(\alpha) every minimizer is the characteristic function of a ball of volume m? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Many-Body Quantum Systems and Effective Theories (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/43, pp. 2465--2511 |
30,003,222 | OWR-14754-006 | Symplectic Reduction of Visible Polar Representations | For a visible polar representation $(G,V)$, is the natural Poisson morphism $(\mathfrak c\oplus\mathfrak c^*)/W\to(V\oplus V^*)\mathbin{///}G$ an isomorphism? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/46, pp. 2625--2691](https://doi.org/10.4171/owr/2016/46)
## Literature review (checked 2026-08-21)
**Status:** open
**Asse... | 3 | open | null | 2,016 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14754-006",
"literature-status:open",
"owr-year:2016"
] | The proposed isomorphism is proved for visible stable locally free polar representations and several other families, but visibility alone does not currently yield a general theorem, so the conjecture remains open. | [
{
"url": "https://doi.org/10.4171/owr/2016/46",
"label": "original conjecture"
},
{
"url": "https://arxiv.org/abs/1609.04573",
"label": "visible stable locally free case"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/46 | null | null | null | For a visible polar representation $(G,V)$, is the natural Poisson morphism $(\mathfrak c\oplus\mathfrak c^*)/W\to(V\oplus V^*)\mathbin{///}G$ an isomorphism? | For a visible polar representation (G,V), is the natural Poisson morphism \mathfrak c\oplus\mathfrak c^*/W\to V\oplus V^*\mathbin{///}G an isomorphism? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Singularities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/46, pp. 2625--2691 |
30,003,223 | OWR-14754-009 | Categorical Functors from Soergel Bimodules to Flag Hilbert Schemes | Do there exist adjoint functors between $K_b(\operatorname{SBim}_n)$ and $D_b(\operatorname{Coh}^T(\operatorname{FHilb}_n(\mathbb{C})))$ such that the forward functor is monoidal and sends $L_1\otimes\cdots\otimes L_{k-1}$ to $C(FT_k)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/46, pp. 2625--2691](https://doi.org/10.4171/owr/2016/46)
## Literature review (checked 2026-08-21)
**Status:** open
**Asse... | 3 | open | null | 2,016 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14754-009",
"literature-status:open",
"owr-year:2016"
] | The proposed adjoint functors between Soergel bimodules and coherent sheaves on the flag Hilbert scheme remain a conjectural categorical construction; later work develops the functor and consequences but does not establish the full stated conjecture. | [
{
"url": "https://doi.org/10.1016/j.aim.2020.107542",
"label": "Gorsky--Negut--Rasmussen, Flag Hilbert schemes"
},
{
"url": "https://doi.org/10.4171/owr/2016/46",
"label": "Oberwolfach Report 46"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/46 | null | null | null | Do there exist adjoint functors between $K_b(\operatorname{SBim}_n)$ and $D_b(\operatorname{Coh}^T(\operatorname{FHilb}_n(\mathbb{C})))$ such that the forward functor is monoidal and sends $L_1\otimes\cdots\otimes L_{k-1}$ to $C(FT_k)$? | Do there exist adjoint functors between K_b(SBim_n) and D_b(Coh^T(FHilb_n(\mathbb C))) such that the forward functor is monoidal and sends L_1\otimes\cdots\otimes L_{k-1} to C(F T_k)? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Singularities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/46, pp. 2625--2691 |
30,003,224 | OWR-14754-010 | Mond's Conjecture for Finite Map Germs | For an $\mathcal A$-finite map germ $f:(\mathbb C^n,S)\to(\mathbb C^{n+1},0)$ in nice dimensions, is the $\mathcal A_e$-codimension of $f$ at most its image Milnor number $\mu_I(f)$, with equality when $f$ is weighted homogeneous? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/46, pp. 2625--2691](https://doi.org/10.4171/owr/2016/46)
## Literature review (checked 2026-08-21)
**Status:** open
**Asse... | 3 | open | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14754-010",
"literature-status:open",
"owr-year:2016"
] | The exact conjecture is not fully reproduced in the extracted record; the record itself says it is known only for n equal to 1 and 2 and remains open for n at least 3, with no later primary proof identified. | [
{
"url": "https://doi.org/10.4171/owr/2016/46",
"label": "Oberwolfach Report 46"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/46 | null | null | null | For an $\mathcal A$-finite map germ $f:(\mathbb C^n,S)\to(\mathbb C^{n+1},0)$ in nice dimensions, is the $\mathcal A_e$-codimension of $f$ at most its image Milnor number $\mu_I(f)$, with equality when $f$ is weighted homogeneous? | For an A-finite map germ f:(\mathbb C^n,S)\to(\mathbb C^{n+1},0) in nice dimensions, is A^e-codim(f)\le\mu_I(f), with equality when f is weighted homogeneous? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Singularities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/46, pp. 2625--2691 |
30,003,225 | OWR-14754-011 | Contact Loci and Nash Sets of Prime Divisors | Let $p_{i_0}$ be a free infinitely near point used to obtain the minimal model of a prime divisor $E$. Is $\bigcup_{E'\equiv_{i_0}E}\mathcal N_{E'}=\operatorname{Cont}_q(E_{p_{i_0}})$ for some $q$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/46, pp. 2625--2691](https://doi.org/10.4171/owr/2016/46)
## Literature review (checked 2026-08-21)
**Status:** open
**Asse... | 3 | open | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14754-011",
"literature-status:open",
"owr-year:2016"
] | The generalized Nash-adjacency problem has been reduced to combinatorics and its relation to plane-curve adjacencies has been clarified, but the specific contact-locus equality proposed in the record is not proved in general. | [
{
"url": "https://doi.org/10.1016/j.aim.2017.09.035",
"label": "Fernandez de Bobadilla--Pere Pereira--Popescu-Pampu, generalized Nash problem"
},
{
"url": "https://doi.org/10.4171/owr/2016/46",
"label": "Oberwolfach Report 46"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/46 | null | null | null | Let $p_{i_0}$ be a free infinitely near point used to obtain the minimal model of a prime divisor $E$. Is $\bigcup_{E'\equiv_{i_0}E}\mathcal N_{E'}=\operatorname{Cont}_q(E_{p_{i_0}})$ for some $q$? | Let p_{i_0} be a free infinitely-near point used to obtain the minimal model of a prime divisor E. Is the union of Nash sets \bigcup_{E'\equiv_{i_0}E}\mathcal N_{E'} equal to \operatorname{Cont}_q(E_{p_{i_0}}) for some q? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Singularities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/46, pp. 2625--2691 |
30,003,226 | OWR-14754-012 | Motivic Poles and Bernstein–Sato Roots | For a polynomial $f$ in $n$ variables, do the poles of its motivic zeta function give zeros of its Bernstein–Sato polynomial? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/46, pp. 2625--2691](https://doi.org/10.4171/owr/2016/46)
## Literature review (checked 2026-08-21)
**Status:** open
**Asse... | 3 | open | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14754-012",
"literature-status:open",
"owr-year:2016"
] | The extracted claim is the general Igusa--Denef--Loeser monodromy conjecture; it has substantial special-case results, but the general polynomial statement remains open, including unresolved surface cases. | [
{
"url": "https://doi.org/10.1007/s00209-019-02342-5",
"label": "On the monodromy conjecture for non-degenerate hypersurfaces"
},
{
"url": "https://doi.org/10.4171/owr/2016/46",
"label": "Oberwolfach Report 46"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/46 | null | null | null | For a polynomial $f$ in $n$ variables, do the poles of its motivic zeta function give zeros of its Bernstein–Sato polynomial? | For a polynomial f in n variables, do the poles of its motivic zeta function give zeros of its Bernstein--Sato polynomial? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Singularities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/46, pp. 2625--2691 |
30,003,227 | OWR-14754-013 | Generators and Support Loci of Bernstein–Sato Ideals | For $F=(f_1,\ldots,f_r):(\mathbb C^n,0)\to(\mathbb C^r,0)$, is the Bernstein–Sato ideal $B_F$ generated by products of linear polynomials $a_1s_1+\cdots+a_rs_r+b$, where $a_i\in\mathbb Q_{\geq0}$ and $b\in\mathbb Q_{>0}$? Is $\operatorname{Exp}(Z(B_F))$ equal to the cohomology-support locus $V_F$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/46, pp. 2625--2691](https://doi.org/10.4171/owr/2016/46)
## Literature review (checked 2026-08-21)
**Status:** open
**Asse... | 3 | open | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14754-013",
"literature-status:open",
"owr-year:2016"
] | The record is an incomplete extraction of the multivariable Bernstein--Sato conjecture, so its full assertion cannot be certified as solved; the unresolved generator statement is treated as open. | [
{
"url": "https://doi.org/10.5802/aif.2939",
"label": "Budur, Bernstein-Sato ideals and local systems"
},
{
"url": "https://doi.org/10.4171/owr/2016/46",
"label": "Oberwolfach Report 46"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/46 | null | null | null | For $F=(f_1,\ldots,f_r):(\mathbb C^n,0)\to(\mathbb C^r,0)$, is the Bernstein–Sato ideal $B_F$ generated by products of linear polynomials $a_1s_1+\cdots+a_rs_r+b$, where $a_i\in\mathbb Q_{\geq0}$ and $b\in\mathbb Q_{>0}$? Is $\operatorname{Exp}(Z(B_F))$ equal to the cohomology-support locus $V_F$? | For F=(f_1,\ldots,f_r):(\mathbb C^n,0)\to(\mathbb C^r,0), is the Bernstein--Sato ideal B_F generated by products of linear polynomials a_1s_1+\cdots+a_rs_r+b, with a_i\in\mathbb Q_{\ge0} and b\in\mathbb Q_{>0}, and is Exp(Z(B_F)) equal to the cohomology-support locus V_F? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Singularities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/46, pp. 2625--2691 |
30,003,228 | OWR-14754-014 | Multivariable Motivic Poles and Monodromy | For a holomorphic germ $F=(f_1,\ldots,f_r):(\mathbb C^n,0)\to(\mathbb C^r,0)$, do all polar hyperplanes of its multivariable motivic zeta function lie in the zero locus $Z(B_F)$ of the Bernstein–Sato ideal? Does the corresponding multivariable monodromy conjecture hold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/46, pp. 2625--2691](https://doi.org/10.4171/owr/2016/46)
## Literature review (checked 2026-08-21)
**Status:** partially so... | 3 | partially_solved | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14754-014",
"literature-status:partially-solved",
"owr-year:2016"
] | Budur--van der Veer--Wu--Zhou prove the exponentiated zero-locus/support-locus equality, but the stronger ideal-generation assertion and the associated multivariable motivic-monodromy conjecture remain unresolved in general. | [
{
"url": "https://doi.org/10.1007/s00222-020-01025-x",
"label": "Budur--van der Veer--Wu--Zhou, Zero loci of Bernstein-Sato ideals"
},
{
"url": "https://doi.org/10.5802/aif.2939",
"label": "Budur, Bernstein-Sato ideals and local systems"
},
{
"url": "https://doi.org/10.4171/owr/2016/46",... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/46 | null | null | null | For a holomorphic germ $F=(f_1,\ldots,f_r):(\mathbb C^n,0)\to(\mathbb C^r,0)$, do all polar hyperplanes of its multivariable motivic zeta function lie in the zero locus $Z(B_F)$ of the Bernstein–Sato ideal? Does the corresponding multivariable monodromy conjecture hold? | For a holomorphic germ F=(f_1,\ldots,f_r):(\mathbb C^n,0)\to(\mathbb C^r,0), with f=\prod_i f_i, conjecture that the multivariable Bernstein--Sato ideal B_F is generated by products of affine forms a_1s_1+\cdots+a_rs_r+b with a_i\in\mathbb Q_{\geq0}, b\in\mathbb Q_{>0}, that Exp(Z(B_F)) equals the cohomology-support lo... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Singularities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/46, pp. 2625--2691 |
30,003,229 | OWR-14754-016 | Stringy Euler Numbers under Mori Flips | If $g:X\dashrightarrow X^+$ is a Mori flip, is $e_{\mathrm{alg}}^{\mathrm{str}}(X)>e_{\mathrm{alg}}^{\mathrm{str}}(X^+)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/46, pp. 2625--2691](https://doi.org/10.4171/owr/2016/46)
## Literature review (checked 2026-08-21)
**Status:** open
**Asse... | 3 | open | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14754-016",
"literature-status:open",
"owr-year:2016"
] | Strict decrease of the algebraic stringy Euler number under arbitrary divisorial Mori contractions or flips is proved for spherical and related equivariant classes, but no general proof or counterexample to the flip assertion was found. | [
{
"url": "https://arxiv.org/abs/1610.03842",
"label": "Batyrev--Gagliardi, On the algebraic stringy Euler number"
},
{
"url": "https://doi.org/10.4171/owr/2016/46",
"label": "Oberwolfach Report 46"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/46 | null | null | null | If $g:X\dashrightarrow X^+$ is a Mori flip, is $e_{\mathrm{alg}}^{\mathrm{str}}(X)>e_{\mathrm{alg}}^{\mathrm{str}}(X^+)$? | If g:X\dashrightarrow X^+ is a Mori flip, then the algebraic stringy Euler number strictly decreases: e_{\mathrm{alg}}^{\mathrm{str}}(X)>e_{\mathrm{alg}}^{\mathrm{str}}(X^+). | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Singularities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/46, pp. 2625--2691 |
30,003,230 | OWR-14754-017 | Stringy Euler Numbers under Divisorial Contractions | If $f:X\to X'$ is a divisorial Mori contraction, is $e_{\mathrm{alg}}^{\mathrm{str}}(X)>e_{\mathrm{alg}}^{\mathrm{str}}(X')$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Singularities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/46, pp. 2625--2691](https://doi.org/10.4171/owr/2016/46)
## Literature review (checked 2026-08-21)
**Status:** partially so... | 3 | partially_solved | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-14754-017",
"literature-status:partially-solved",
"owr-year:2016"
] | The flip inequality is established in the equivariant Mori program for projective spherical varieties, but the unrestricted conjecture in the record remains open. | [
{
"url": "https://arxiv.org/abs/1610.03842",
"label": "Batyrev--Gagliardi, On the algebraic stringy Euler number"
},
{
"url": "https://doi.org/10.4171/owr/2016/46",
"label": "Oberwolfach Report 46"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/46 | null | null | null | If $f:X\to X'$ is a divisorial Mori contraction, is $e_{\mathrm{alg}}^{\mathrm{str}}(X)>e_{\mathrm{alg}}^{\mathrm{str}}(X')$? | If f:X\to X' is a divisorial Mori contraction, then the algebraic stringy Euler number strictly decreases: e_{\mathrm{alg}}^{\mathrm{str}}(X)>e_{\mathrm{alg}}^{\mathrm{str}}(X'). | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Singularities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/46, pp. 2625--2691 |
30,003,231 | OWR-15169-001 | Littlewood's Simultaneous Approximation Conjecture | For every $(x,y)\in\mathbb R^2$, does $\liminf_{n\to\infty}n\|nx\|\,\|ny\|=0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometry and Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/48, pp. 2749--2792](https://doi.org/10.4171/owr/2016/48)
## ... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15169-001",
"literature-status:open",
"owr-year:2016"
] | Littlewood's conjecture for pairs of real numbers remains open; the bounded-trajectory reformulation and many exceptional-set results do not settle the universal liminf assertion. | [
{
"url": "https://doi.org/10.4171/owr/2016/48",
"label": "Oberwolfach Report 48"
},
{
"url": "https://arxiv.org/abs/2211.04523",
"label": "Fregoli--Kleinbock, On multiplicatively badly approximable vectors"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/48 | null | null | null | For every $(x,y)\in\mathbb R^2$, does $\liminf_{n\to\infty}n\|nx\|\,\|ny\|=0$? | For every (x,y)\in\mathbb R^2, does Littlewood's conjecture hold, namely \liminf_{n\to\infty}n \|nx\| \|ny\|=0? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometry and Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/48, pp. 2749--2792 |
30,003,232 | OWR-15169-006 | Hausdorff Dimension of Intersections of Badly Approximable Sets | For any specified system of Diophantine inequalities defining a generalized badly approximable set $\operatorname{Bad}$, does $\operatorname{Bad}$ have full Hausdorff dimension? More generally, for a countable family $\operatorname{Bad}_1,\operatorname{Bad}_2,\ldots$, determine the size and Hausdorff dimension of $\big... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometry and Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/48, pp. 2749--2792](https://doi.org/10.4171/owr/2016/48)
## ... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15169-006",
"literature-status:open",
"owr-year:2016"
] | The extracted item is only a continuation labelled conjecture and does not identify a standalone universal assertion; the surrounding generalized-Cantor method gives tools and special cases, not a complete resolution of the implied problem. | [
{
"url": "https://doi.org/10.4171/owr/2016/48",
"label": "Oberwolfach Report 48"
},
{
"url": "https://arxiv.org/abs/1007.1848",
"label": "Badziahin--Velani, multiplicative approximation and generalized Cantor sets"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/48 | null | null | null | For any specified system of Diophantine inequalities defining a generalized badly approximable set $\operatorname{Bad}$, does $\operatorname{Bad}$ have full Hausdorff dimension? More generally, for a countable family $\operatorname{Bad}_1,\operatorname{Bad}_2,\ldots$, determine the size and Hausdorff dimension of $\big... | For a specified notion of badly approximable vectors with set Bad, determine whether Bad has full Hausdorff dimension; more generally, for a countable family Bad_1,Bad_2,\ldots, determine the size or Hausdorff dimension of \bigcap_{i=1}^{\infty}Bad_i. | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometry and Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/48, pp. 2749--2792 |
30,003,233 | OWR-15169-007 | Multiplicatively Badly Approximable Pairs | What is the correct multiplicative analogue of badly approximable points? For $M_\lambda=\{(\alpha,\beta)\in\mathbb R^2:\liminf_{q\to\infty}q(\log q)^\lambda\|q\alpha\|\,\|q\beta\|>0\}$, is $M_\lambda$ empty for $\lambda<1$ and of full Hausdorff dimension for $\lambda\geq1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometry and Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/48, pp. 2749--2792](https://doi.org/10.4171/owr/2016/48)
## ... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15169-007",
"literature-status:open",
"owr-year:2016"
] | The multiplicative notion of badly approximable pairs is tied to Littlewood's still-open conjecture; logarithmic-factor constructions provide large exceptional sets but do not answer the zero-factor problem. | [
{
"url": "https://arxiv.org/abs/1101.1855",
"label": "Badziahin, On multiplicatively badly approximable numbers"
},
{
"url": "https://doi.org/10.4171/owr/2016/48",
"label": "Oberwolfach Report 48"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/48 | null | null | null | What is the correct multiplicative analogue of badly approximable points? For $M_\lambda=\{(\alpha,\beta)\in\mathbb R^2:\liminf_{q\to\infty}q(\log q)^\lambda\|q\alpha\|\,\|q\beta\|>0\}$, is $M_\lambda$ empty for $\lambda<1$ and of full Hausdorff dimension for $\lambda\geq1$? | What is the correct multiplicative analogue of badly approximable points? In particular, for M_\lambda=\{(\alpha,\beta)\in\mathbb R^2:\liminf_{q\to\infty}q(\log q)^\lambda\|q\alpha\|\|q\beta\|>0\}, determine whether M_\lambda is empty for \lambda<1 and has full Hausdorff dimension for \lambda\geq1. | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometry and Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/48, pp. 2749--2792 |
30,003,234 | OWR-15169-008 | Badly Approximable Points on Planar Curves | For weights $i, j \geq 0$ with $i + j = 1$, let $\operatorname{Bad}(i, j) \subset \mathbb{R}^2$ denote the set of $(i, j)$-badly approximable points in the plane, i.e., pairs $(x, y)$ for which there exists $c > 0$ such that $\max(q^i \|qx\|, q^j \|qy\|) \geq c$ for all integers $q \geq 1$. Given a nondegenerate planar... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometry and Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/48, pp. 2749--2792](https://doi.org/10.4171/owr/2016/48)
## ... | 3 | partially_solved | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15169-008",
"literature-status:partially-solved",
"owr-year:2016"
] | Davenport's question is solved for twice-differentiable non-degenerate planar curves, where the intersection has full curve dimension, and for several lines; arbitrary planar curves still include unresolved or empty cases. | [
{
"url": "https://doi.org/10.1007/s00208-014-1020-z",
"label": "Badziahin--Velani, badly approximable points on planar curves"
},
{
"url": "https://doi.org/10.4171/owr/2016/48",
"label": "Oberwolfach Report 48"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/48 | null | null | null | For weights $i, j \geq 0$ with $i + j = 1$, let $\operatorname{Bad}(i, j) \subset \mathbb{R}^2$ denote the set of $(i, j)$-badly approximable points in the plane, i.e., pairs $(x, y)$ for which there exists $c > 0$ such that $\max(q^i \|qx\|, q^j \|qy\|) \geq c$ for all integers $q \geq 1$. Given a nondegenerate planar... | Given a planar curve C and weights i,j\geq0 with i+j=1, is C\cap\operatorname{Bad}(i,j) uncountable? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometry and Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/48, pp. 2749--2792 |
30,003,235 | OWR-15169-009 | Weighted Bad Approximation on Affine Lines | For $L_{a,b}=\{(x,ax+b):x\in\mathbb R\}$, weights $i,j\geq0$ with $i+j=1$, and $\sigma=\min\{i,j\}$, can the known hypothesis $\liminf_{q\to\infty}q^{1/\sigma-\varepsilon}\max\{\|qa\|,\|qb\|\}>0$ for some $\varepsilon>0$ be relaxed to $\varepsilon=0$ while retaining $\dim_H(L_{a,b}\cap\operatorname{Bad}(i,j))=1$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometry and Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/48, pp. 2749--2792](https://doi.org/10.4171/owr/2016/48)
## ... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15169-009",
"literature-status:open",
"owr-year:2016"
] | The cited Jacobian-rank theorem proves uncountability under the full-rank hypothesis, but the proposed relaxation to zero excess dimension is not established by the later curve and manifold results located. | [
{
"url": "https://doi.org/10.4171/owr/2016/48",
"label": "Oberwolfach Report 48"
},
{
"url": "https://arxiv.org/abs/2005.02128",
"label": "Beresnevich--Nesharim--Yang, winning on curves"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/48 | null | null | null | For $L_{a,b}=\{(x,ax+b):x\in\mathbb R\}$, weights $i,j\geq0$ with $i+j=1$, and $\sigma=\min\{i,j\}$, can the known hypothesis $\liminf_{q\to\infty}q^{1/\sigma-\varepsilon}\max\{\|qa\|,\|qb\|\}>0$ for some $\varepsilon>0$ be relaxed to $\varepsilon=0$ while retaining $\dim_H(L_{a,b}\cap\operatorname{Bad}(i,j))=1$? | For L_{a,b}=\{(x,ax+b):x\in\mathbb R\}, weights i,j\geq0 with i+j=1, and \sigma=\min\{i,j\}, can the known hypothesis \liminf_{q\to\infty}q^{1/\sigma-\varepsilon}\max\{\|qa\|,\|qb\|\}>0 for some \varepsilon>0 be relaxed to \varepsilon=0 while retaining dim_H(L_{a,b}\cap\operatorname{Bad}(i,j))=1? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometry and Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/48, pp. 2749--2792 |
30,003,236 | OWR-15169-010 | Intrinsic Diophantine Exponents of Submanifolds | For a nondegenerate $k$-dimensional submanifold $M\subset\mathbb R^d$, define
$$
\omega(M)=\inf_{x\in M}\limsup_{p/q\in M}\frac{-\log|x-p/q|}{\log q},
$$
and let $\omega(k,d)$ be the supremum over such $M$. Can the available upper bound be improved, can $\omega(k,d)$ be computed exactly for more pairs $(k,d)$, and does... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometry and Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/48, pp. 2749--2792](https://doi.org/10.4171/owr/2016/48)
## ... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15169-010",
"literature-status:open",
"owr-year:2016"
] | The record asks several strengthening and exact-value questions for intrinsic Diophantine exponents; known formulas and upper bounds do not settle the requested improvements or the essential-infimum equality in general. | [
{
"url": "https://doi.org/10.1007/s00222-015-0586-8",
"label": "Beresnevich--Velani, Badly approximable points on manifolds"
},
{
"url": "https://doi.org/10.4171/owr/2016/48",
"label": "Oberwolfach Report 48"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/48 | null | null | null | For a nondegenerate $k$-dimensional submanifold $M\subset\mathbb R^d$, define
$$
\omega(M)=\inf_{x\in M}\limsup_{p/q\in M}\frac{-\log|x-p/q|}{\log q},
$$
and let $\omega(k,d)$ be the supremum over such $M$. Can the available upper bound be improved, can $\omega(k,d)$ be computed exactly for more pairs $(k,d)$, and does... | For a nondegenerate k-dimensional submanifold M\subset\mathbb R^d, define \omega(M)=\inf_{x\in M}\limsup_{p/q\in M}[-\log|x-p/q|]/\log q and let \omega(k,d) be the supremum over such M; can the known upper bound be improved, can \omega(k,d) be computed exactly for more (k,d), and does the essential-infimum variant \ome... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometry and Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/48, pp. 2749--2792 |
30,003,237 | OWR-15169-011 | Khintchine Theory for Symbolic Self-Similar Approximation | Let $\phi_1,\ldots,\phi_N$ be contractions of $\mathbb R^n$ with attractor $F$, choose $x\in F$ and an approximating function $\psi$ on finite words, and let $W(x,\psi)$ be the set of points of $F$ lying in
$$
B\bigl(\phi_{s_1}\circ\cdots\circ\phi_{s_k}(x),\psi(s_1,\ldots,s_k)\bigr)
$$
for infinitely many words. Classi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometry and Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/48, pp. 2749--2792](https://doi.org/10.4171/owr/2016/48)
## ... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15169-011",
"literature-status:open",
"owr-year:2016"
] | Recent work proves Khintchine-type dichotomies for important self-similar and Cantor systems, but the arbitrary symbolic contraction system and arbitrary word-dependent approximation function in the record are not classified completely. | [
{
"url": "https://arxiv.org/abs/2409.08061",
"label": "Benard--He--Zhang, Khintchine dichotomy for self-similar measures"
},
{
"url": "https://doi.org/10.1007/s00208-023-02608-8",
"label": "Intrinsic Diophantine approximation for overlapping IFS"
},
{
"url": "https://doi.org/10.4171/owr/... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/48 | null | null | null | Let $\phi_1,\ldots,\phi_N$ be contractions of $\mathbb R^n$ with attractor $F$, choose $x\in F$ and an approximating function $\psi$ on finite words, and let $W(x,\psi)$ be the set of points of $F$ lying in
$$
B\bigl(\phi_{s_1}\circ\cdots\circ\phi_{s_k}(x),\psi(s_1,\ldots,s_k)\bigr)
$$
for infinitely many words. Classi... | Let \phi_1,\ldots,\phi_N be contractions of \mathbb R^n with attractor F, choose x\in F and an approximating function \psi on finite words, and set W(x,\psi)=\{y\in F:y\in B(\phi_{s_1}\circ\cdots\circ\phi_{s_k}(x),\psi(s_1,\ldots,s_k)) for infinitely many words\}; classify the \psi for which W(x,\psi) is large and dete... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometry and Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/48, pp. 2749--2792 |
30,003,238 | OWR-15169-012 | Removing Logarithmic Losses in Multiplicative Approximation | The sets $\{(\alpha,\beta):\liminf_{q\to\infty}(q\log q\log\log q)\lVert q\alpha\rVert\lVert q\beta\rVert>0\}$ and $\{\alpha:\liminf_{q\to\infty}(q\log q\log\log q)|q|_p\lVert q\alpha\rVert>0\}$ have full Hausdorff dimension. Can the factor $\log\log q$ be removed? Are these sets winning? What happens when they are int... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometry and Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/48, pp. 2749--2792](https://doi.org/10.4171/owr/2016/48)
## ... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15169-012",
"literature-status:open",
"owr-year:2016"
] | Logarithmic-factor constructions give full-dimensional sets, but dropping the extra log log factor, proving the relevant winning property, and obtaining the planar-curve intersection remain open in the stated generality. | [
{
"url": "https://arxiv.org/abs/1101.1855",
"label": "Badziahin, On multiplicatively badly approximable numbers"
},
{
"url": "https://doi.org/10.4171/owr/2016/48",
"label": "Oberwolfach Report 48"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/48 | null | null | null | The sets $\{(\alpha,\beta):\liminf_{q\to\infty}(q\log q\log\log q)\lVert q\alpha\rVert\lVert q\beta\rVert>0\}$ and $\{\alpha:\liminf_{q\to\infty}(q\log q\log\log q)|q|_p\lVert q\alpha\rVert>0\}$ have full Hausdorff dimension. Can the factor $\log\log q$ be removed? Are these sets winning? What happens when they are int... | The sets \{(\alpha,\beta):\liminf_{q\to\infty}(q\log q\log\log q)\|q\alpha\|\|q\beta\|>0\} and \{\alpha:\liminf_{q\to\infty}(q\log q\log\log q)|q|_p\|q\alpha\|>0\} have full Hausdorff dimension; can the factor \log\log q be removed, are these sets winning, and what happens on intersection with a planar curve? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Arbeitsgemeinschaft: Diophantine Approximation, Fractal Geometry and Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/48, pp. 2749--2792 |
30,003,239 | OWR-15170-001 | Brauer–Manin Obstructions for Rationally Connected Fibrations | Let $k$ be a number field and $f:X\to\mathbb P^1_k$ a projective surjective morphism with geometrically rationally connected generic fibre. If the Brauer–Manin obstruction is the only obstruction to the Hasse principle for every smooth fibre of $f$, is it also the only obstruction for $X$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | partially_solved | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-001",
"literature-status:partially-solved",
"owr-year:2016"
] | Harpaz--Wittenberg prove the zero-cycle analogue for rationally connected fibrations and rational-point results under a polynomial-value conjecture; unconditional rational-point density is known in substantial norm-form and few-fibre cases, but the full question remains open. | [
{
"url": "https://doi.org/10.4007/annals.2016.183.1.5",
"label": "Harpaz--Wittenberg, fibration method for zero-cycles and rational points"
},
{
"url": "https://doi.org/10.24033/asens.2348",
"label": "Browning--Matthiesen, norm forms"
},
{
"url": "https://doi.org/10.1515/crelle-2022-0042... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | Let $k$ be a number field and $f:X\to\mathbb P^1_k$ a projective surjective morphism with geometrically rationally connected generic fibre. If the Brauer–Manin obstruction is the only obstruction to the Hasse principle for every smooth fibre of $f$, is it also the only obstruction for $X$? | Let k be a number field and f:X\to\mathbb P^1_k a projective surjective morphism with geometrically rationally connected generic fibre. If the Brauer--Manin obstruction is the only obstruction to the Hasse principle for every smooth fibre of f, is it also the only obstruction for the total space X? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,240 | OWR-15170-002 | Definability of Evaluation in Rings of Entire Functions | For the rings $H_{t_1,t_2}(\mathbb C^2)$ of entire functions and their meromorphic fraction fields $M_{t_1,t_2}(\mathbb C^2)$, is the evaluation predicate positive-existentially definable in the corresponding ring language? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | open | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-002",
"literature-status:open",
"owr-year:2016"
] | The positive-existential Eval questions remain open; the report's negative result concerns a different differential-equation variant. | [
{
"url": "https://ems.press/content/serial-article-files/46652",
"label": "Oberwolfach Reports 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | For the rings $H_{t_1,t_2}(\mathbb C^2)$ of entire functions and their meromorphic fraction fields $M_{t_1,t_2}(\mathbb C^2)$, is the evaluation predicate positive-existentially definable in the corresponding ring language? | For the rings H_{t_1,t_2}(\mathbb C^2) of entire functions and their meromorphic fraction field M_{t_1,t_2}(\mathbb C^2), is the evaluation predicate positive-existentially definable in the corresponding ring language (with the ordinary valuation predicate in the meromorphic case); more generally, is there an algorithm... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,241 | OWR-15170-003 | Decidability of Analytic Solutions to Algebraic Equations | Is there an algorithm which, given an algebraic equation in one or more variables with coefficients in $\mathbb Z[z]$, decides whether it has a solution analytic at $0$, on an open superset of the unit disc, or on the whole complex plane? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | open | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-003",
"literature-status:open",
"owr-year:2016"
] | The algorithmic question for algebraic equations without differentiation is explicitly reported as open, with no later resolution located. | [
{
"url": "https://ems.press/content/serial-article-files/46652",
"label": "Oberwolfach Reports 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | Is there an algorithm which, given an algebraic equation in one or more variables with coefficients in $\mathbb Z[z]$, decides whether it has a solution analytic at $0$, on an open superset of the unit disc, or on the whole complex plane? | Is there an algorithm which, given an algebraic equation in one or more variables with coefficients in \mathbb Z[z], decides whether it has a solution analytic at 0, analytic on an open superset of the unit disc, or analytic on the whole complex plane? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,242 | OWR-15170-004 | Northcott Property for Bounded-Degree Composita | Let $\mathbb Q^{(d)}$ be the compositum of all extensions of $\mathbb Q$ of degree at most $d$; does it have Property (N), meaning that for every $X\geq1$ only finitely many elements have absolute multiplicative Weil height $H(\alpha)<X$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | [
"OWR-15170-005"
] | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-004",
"literature-status:open",
"owr-year:2016"
] | Property (N) for the infinite extension Q(d) remains an open Northcott-property problem for d\geq 3. | [
{
"url": "https://arxiv.org/abs/2310.11337",
"label": "Widmer, Northcott property"
},
{
"url": "https://ems.press/content/serial-article-files/46652",
"label": "Oberwolfach Reports 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | Let $\mathbb Q^{(d)}$ be the compositum of all extensions of $\mathbb Q$ of degree at most $d$; does it have Property (N), meaning that for every $X\geq1$ only finitely many elements have absolute multiplicative Weil height $H(\alpha)<X$? | Let \mathbb Q^{(d)} be the compositum of all extensions of \mathbb Q of degree at most d; does \mathbb Q^{(d)} have Property (N), meaning that for every X\geq1 only finitely many elements have absolute multiplicative Weil height H(\alpha)<X? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,243 | OWR-15170-005 | Duplicate Northcott-Property Question | For every positive integer d, does \mathbb Q^{(d)} have Property (N), i.e. are there only finitely many \alpha\in\mathbb Q^{(d)} with H(\alpha)<X for each X\geq1? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Duplicate/merged OWR extraction (This extraction duplicates the bounded-degree-composita Northcott question represented canonically by OWR-15170-004. No separate clean state) | [
"OWR-15170-004"
] | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-005",
"literature-status:open",
"owr-year:2016"
] | The cited question of Property (N) for Q(d) remains unresolved for every d\geq 3. | [
{
"url": "https://arxiv.org/abs/2310.11337",
"label": "Widmer, Northcott property"
},
{
"url": "https://ems.press/content/serial-article-files/46652",
"label": "Oberwolfach Reports 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | null | For every positive integer d, does \mathbb Q^{(d)} have Property (N), i.e. are there only finitely many \alpha\in\mathbb Q^{(d)} with H(\alpha)<X for each X\geq1? | unrecoverable | This extraction duplicates the bounded-degree-composita Northcott question represented canonically by OWR-15170-004. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,244 | OWR-15170-006 | Northcott Property for Totally Real Integer Rings | For the ring of integers $\mathcal O_{\mathbb Q_{\mathrm{tr}}^{(d)}}$ of the maximal totally real subfield of $\mathbb Q^{(d)}$, does Property (N) hold? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-006",
"literature-status:open",
"owr-year:2016"
] | Whether the totally real ring OQ(d)_{\mathrm{tr}} has Property (N) is still treated as an open Northcott-property question. | [
{
"url": "https://ems.press/content/serial-article-files/46652",
"label": "Oberwolfach Reports 2017"
},
{
"url": "https://doi.org/10.1112/jlms.70022",
"label": "Daans et al., Universal quadratic forms"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | For the ring of integers $\mathcal O_{\mathbb Q_{\mathrm{tr}}^{(d)}}$ of the maximal totally real subfield of $\mathbb Q^{(d)}$, does Property (N) hold? | For the ring of integers \mathcal O_{\mathbb Q_{\mathrm{tr}}^{(d)}} of the maximal totally real subfield of \mathbb Q^{(d)}, does Property (N) hold? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,245 | OWR-15170-007 | Bounded-House Finiteness for Totally Real Algebraic Integers | For the ring $\mathcal O_{\mathbb Q_{\mathrm{tr}}^{(d)}}$ of totally real algebraic integers, is $\{\alpha:|\alpha|<X\}$ finite for every $X\geq1$, where $|\alpha|$ is the maximum modulus of the conjugates of $\alpha$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-007",
"literature-status:open",
"owr-year:2016"
] | The finiteness assertion for bounded house in OQ(d)_{\mathrm{tr}} is part of the still-hard Northcott-property problem; no proof of the stated finiteness was found. | [
{
"url": "https://doi.org/10.1112/jlms.70022",
"label": "Daans et al., Universal quadratic forms"
},
{
"url": "https://ems.press/content/serial-article-files/46652",
"label": "Oberwolfach Reports 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | For the ring $\mathcal O_{\mathbb Q_{\mathrm{tr}}^{(d)}}$ of totally real algebraic integers, is $\{\alpha:|\alpha|<X\}$ finite for every $X\geq1$, where $|\alpha|$ is the maximum modulus of the conjugates of $\alpha$? | For the ring \mathcal O_{\mathbb Q_{\mathrm{tr}}^{(d)}} of totally real algebraic integers, is \{\alpha:|\alpha|<X\} finite for every X\geq1, where |\alpha| is the maximum modulus of the conjugates of \alpha? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,246 | OWR-15170-008 | Sharp Transcendence Bounds for the Modular J-Function | Let $C$ be $j\operatorname{cl}$-closed, let $\lambda$ be a $j\operatorname{cl}$-independent tuple, and set $F=\mathbb Q(\lambda)$. For a tuple $z$ whose coordinates lie in distinct $G$-orbits and a nonscalar $g\in G_F\setminus G$, is the Ax–Schanuel lower bound
$$
\operatorname{td}\bigl(j(z),j'(z),j''(z),j(gz),j'(gz),j... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | partially_solved | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-008",
"literature-status:partially-solved",
"owr-year:2016"
] | Later work gives conditional and structural advances, including a pregeometry result, but neither the sharp inequality nor the requested full explicit description is established. | [
{
"url": "https://doi.org/10.1007/s00208-024-03082-6",
"label": "Eterović, Generic solutions"
},
{
"url": "https://ueaeprints.uea.ac.uk/80428/1/Extending_j_derivations.pdf",
"label": "Extending j-derivations"
},
{
"url": "https://ems.press/content/serial-article-files/46652",
"label"... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | Let $C$ be $j\operatorname{cl}$-closed, let $\lambda$ be a $j\operatorname{cl}$-independent tuple, and set $F=\mathbb Q(\lambda)$. For a tuple $z$ whose coordinates lie in distinct $G$-orbits and a nonscalar $g\in G_F\setminus G$, is the Ax–Schanuel lower bound
$$
\operatorname{td}\bigl(j(z),j'(z),j''(z),j(gz),j'(gz),j... | In the model theory of the j-function, is the transcendence-degree lower bound td( j(z),j'(z),j''(z),j(gz),j'(gz),j''(gz)/F,C )\geq3n of the main theorem sharp or improvable without proving modular Schanuel conjectures, and can the j-derivation pregeometry jcl be described explicitly? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,247 | OWR-15170-009 | Hilbert's Tenth Problem in Generic Rational Subrings | Does there exist an HTP-generic subring of $\mathbb Q$ with a Diophantine model of $(\mathbb Z,+,\cdot)$, and does there exist a polynomial $f$ with $\mu(B(f))>0$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | open | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-009",
"literature-status:open",
"owr-year:2016"
] | The HTP-generic subring and positive-boundary-measure questions remain conjectural; no demonstrable resolution of the stated measure assertion was found. | [
{
"url": "https://ems.press/content/serial-article-files/46652",
"label": "Oberwolfach Reports 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | Does there exist an HTP-generic subring of $\mathbb Q$ with a Diophantine model of $(\mathbb Z,+,\cdot)$, and does there exist a polynomial $f$ with $\mu(B(f))>0$? | Does there exist an HTP-generic subring of \mathbb Q in which there is a Diophantine model of (\mathbb Z,+,\cdot), and does there exist a polynomial f with positive measure boundary set \mu(B(f))>0? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,248 | OWR-15170-010 | HTP-Complete Polynomials over Rational Subrings | Which subrings $R_W\subset\mathbb Q$ have an HTP-complete polynomial, meaning one that uniformly encodes solvability in $R_W$ of every polynomial equation over $\mathbb Q$, and which have an effectively HTP-complete polynomial with a computable encoding map? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | open | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-010",
"literature-status:open",
"owr-year:2016"
] | The characterization of subrings of Q admitting effectively HTP-complete polynomials remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46652",
"label": "Oberwolfach Reports 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | Which subrings $R_W\subset\mathbb Q$ have an HTP-complete polynomial, meaning one that uniformly encodes solvability in $R_W$ of every polynomial equation over $\mathbb Q$, and which have an effectively HTP-complete polynomial with a computable encoding map? | Which subrings R_W\subset\mathbb Q have an HTP-complete polynomial, meaning one that uniformly encodes the solvability in R_W of every polynomial equation over \mathbb Q, and which have an effectively HTP-complete polynomial with a computable encoding map? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,249 | OWR-15170-011 | Existential Theory of Polynomial Rings with Divisibility | Is the existential theory of $\mathbb F_q[t]$ in the language of addition, divisibility, and the predicate for powers of $t$ decidable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | partially_solved | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-011",
"literature-status:partially-solved",
"owr-year:2016"
] | The one-existential-quantifier fragment is decidable, but the full existential theory in the stated language remains open. | [
{
"url": "https://jaf.lacl.fr/JAF27/alla.pdf",
"label": "Sirokofskich, Weak Divisibility"
},
{
"url": "https://ems.press/content/serial-article-files/46652",
"label": "Oberwolfach Reports 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | Is the existential theory of $\mathbb F_q[t]$ in the language of addition, divisibility, and the predicate for powers of $t$ decidable? | Is the existential theory of \mathbb F_q[t] in the language of addition, divisibility, and the predicate for powers of t decidable? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,250 | OWR-15170-014 | $p$-Adic Definability Rings with Finite Additive Descriptions | For a prime $p$, with $\gamma_p(x)=p^{-1}(x^p-x)/((x^p-x)^2-1)$ and $\Gamma_p(\mathbb Q)=\{a(1+pb)^{-1}:a,b\in\mathbb Z_{(p)}[\gamma_p(\mathbb Q)]\}$, does there exist $n_p$ such that $\Gamma_p(\mathbb Q)=\{a(1+pb)^{-1}:a,b\in\sum_{i=1}^{n_p}\gamma_p(\mathbb Q)\}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | partially_solved | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-014",
"literature-status:partially-solved",
"owr-year:2016"
] | The existence theorem is proved, but the problem's requested direct constructive proof and explicit bounds remain unavailable. | [
{
"url": "https://doi.org/10.1002/mana.201900173",
"label": "Anscombe--Dittmann--Fehm, p-adic Siegel theorem"
},
{
"url": "https://ems.press/content/serial-article-files/46652",
"label": "Oberwolfach Reports 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | For a prime $p$, with $\gamma_p(x)=p^{-1}(x^p-x)/((x^p-x)^2-1)$ and $\Gamma_p(\mathbb Q)=\{a(1+pb)^{-1}:a,b\in\mathbb Z_{(p)}[\gamma_p(\mathbb Q)]\}$, does there exist $n_p$ such that $\Gamma_p(\mathbb Q)=\{a(1+pb)^{-1}:a,b\in\sum_{i=1}^{n_p}\gamma_p(\mathbb Q)\}$? | For a prime p, with \gamma_p(x)=p^{-1}(x^p-x)/((x^p-x)^2-1) and \Gamma_p(\mathbb Q)=\{a(1+pb)^{-1}:a,b\in\mathbb Z_{(p)}[\gamma_p(\mathbb Q)]\}, does there exist n_p such that \Gamma_p(\mathbb Q)=\{a(1+pb)^{-1}:a,b\in\sum_{i=1}^{n_p}\gamma_p(\mathbb Q)\}? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,251 | OWR-15170-018 | Infinitude of Twin Primes | Are there infinitely many twin-prime pairs; equivalently, for every $n$, are there at least $n$ pairs of primes differing by $2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-018",
"literature-status:open",
"owr-year:2016"
] | The assertion is equivalent to the twin-prime conjecture and remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46652",
"label": "Oberwolfach Reports 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | Are there infinitely many twin-prime pairs; equivalently, for every $n$, are there at least $n$ pairs of primes differing by $2$? | Are there infinitely many twin-prime pairs, equivalently, for every n are there at least n pairs of primes differing by 2? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,252 | OWR-15170-019 | Büchi's Problem for Sequences of Integer Squares | Does there exist a positive integer $M$ such that every sequence of $M$ integer squares with second differences equal to $2$ is necessarily of the form $(x+i)^2$ for some $x\in\mathbb Z$ and $1\leq i\leq M$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | partially_solved | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-019",
"literature-status:partially-solved",
"owr-year:2016"
] | Büchi's problem remains open in general, but recent work proves nontrivial finite-length cases, including a five-square result. | [
{
"url": "https://arxiv.org/abs/2412.16740",
"label": "Recent progress on Büchi's problem"
},
{
"url": "https://www.mathnet.ru/rus/znsl3818",
"label": "Pasten--Pheidas--Vidaux survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | Does there exist a positive integer $M$ such that every sequence of $M$ integer squares with second differences equal to $2$ is necessarily of the form $(x+i)^2$ for some $x\in\mathbb Z$ and $1\leq i\leq M$? | Does there exist a positive integer M such that every sequence of M integer squares with second differences equal to 2 is necessarily of the form (x+i)^2, for some x in Z and 1<=i<=M? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,253 | OWR-15170-020 | Differential Criteria for Low-Genus Curves on Surfaces | Let $X$ be a smooth projective surface over $\mathbb C$, let $\pi:X\to\mathbb P^2$ be a finite morphism with branch divisor $B$, and fix $g\geq0$. If $L$ is an invertible sheaf of minimal degree among those admitting a nonzero section vanishing on the image of every curve on $X$ of geometric genus at most $g$, does the... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | partially_solved | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-020",
"literature-status:partially-solved",
"owr-year:2016"
] | Surface-level criteria for completeness of the integral-curve list are known, but the general hypotheses and higher-dimensional extension requested here remain unresolved. | [
{
"url": "https://qspace.library.queensu.ca/bitstreams/007eb1de-ecf4-4747-a756-f7cac789ba56/download",
"label": "García-Fritz, Curves on surfaces"
},
{
"url": "https://ems.press/content/serial-article-files/46652",
"label": "Oberwolfach Reports 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | Let $X$ be a smooth projective surface over $\mathbb C$, let $\pi:X\to\mathbb P^2$ be a finite morphism with branch divisor $B$, and fix $g\geq0$. If $L$ is an invertible sheaf of minimal degree among those admitting a nonzero section vanishing on the image of every curve on $X$ of geometric genus at most $g$, does the... | Which hypotheses on a surface X over C, expressed through the branch divisor B of a morphism X to P^2 and an invertible sheaf L, guarantee a section omega in H^0(P^2,L tensor S^r Omega^1_{P^2/C}) whose omega-integral curves include all components of B and make the low-genus curve method work? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,254 | OWR-15170-021 | Completeness Tests for Integral Subvarieties | Given a smooth projective variety $X$ over $\mathbb C$ of dimension greater than two and $\omega\in H^0(X,L\otimes S^r\Omega^1_{X/\mathbb C})$, how can one check that a listed collection of $\omega$-integral curves or hypersurfaces contains all such curves or hypersurfaces of $X$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | partially_solved | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-021",
"literature-status:partially-solved",
"owr-year:2016"
] | Completeness criteria are available in dimension two, but no general method for checking completeness of the higher-dimensional list is known. | [
{
"url": "https://qspace.library.queensu.ca/bitstreams/007eb1de-ecf4-4747-a756-f7cac789ba56/download",
"label": "García-Fritz, Curves on surfaces"
},
{
"url": "https://ems.press/content/serial-article-files/46652",
"label": "Oberwolfach Reports 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | Given a smooth projective variety $X$ over $\mathbb C$ of dimension greater than two and $\omega\in H^0(X,L\otimes S^r\Omega^1_{X/\mathbb C})$, how can one check that a listed collection of $\omega$-integral curves or hypersurfaces contains all such curves or hypersurfaces of $X$? | Given a smooth projective variety X over C of dimension greater than two and omega in H^0(X,L tensor S^r Omega^1_{X/C}), how can one check that a listed collection of omega-integral curves or hypersurfaces contains all such curves or hypersurfaces of X? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,255 | OWR-15170-022 | Extremality Criteria for Positive-Characteristic Valued Fields | For a valued field $(K,v)$ of positive residue characteristic, with value group a $\mathbb Z$-group or with divisible value group and large imperfect residue field, is there a simple useful additional assumption ensuring that $(K,v)$ is extremal? More generally, is every maximal valued field with a $\mathbb Z$-group as... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | open | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-022",
"literature-status:open",
"owr-year:2016"
] | There is no complete characterization of extremal valued fields in positive residue characteristic under the stated residue-field and value-group conditions. | [
{
"url": "https://arxiv.org/abs/1407.3759",
"label": "Anscombe--Kuhlmann, Extremal valued fields"
},
{
"url": "https://fvkuhlmann.de/EXTRNOT.pdf",
"label": "Kuhlmann, Extremal valued fields notes"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | For a valued field $(K,v)$ of positive residue characteristic, with value group a $\mathbb Z$-group or with divisible value group and large imperfect residue field, is there a simple useful additional assumption ensuring that $(K,v)$ is extremal? More generally, is every maximal valued field with a $\mathbb Z$-group as... | For a valued field (K,v) of positive residue characteristic, with value group a Z-group or with divisible value group and large imperfect residue field, is there a simple useful additional assumption that ensures (K,v) is extremal? More generally, is every maximal valued field with value group a Z-group or with divisib... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,256 | OWR-15170-023 | Definability in Automata-Presentable Ring Expansions | Let $R$ be a Euclidean ring with Euclidean function $\delta$, let $\preccurlyeq$ be the preorder induced by $\delta$, and for a noninvertible $r\in R$ let $V_r$ denote the highest power of $r$ dividing an element and $\mathbin{\cdot_r}$ the multiplication relation restricted according to powers of $r$. For multiplicati... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | open | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-023",
"literature-status:open",
"owr-year:2016"
] | The common-definability characterization and decidability of the algebraic power-series structure remain open; known polynomial-ring expansions do not settle these questions. | [
{
"url": "https://doi.org/10.1080/00927872.2015.1028236",
"label": "Point--Rigo--Waxweiler, Polynomial rings"
},
{
"url": "https://ems.press/content/serial-article-files/46652",
"label": "Oberwolfach Reports 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | Let $R$ be a Euclidean ring with Euclidean function $\delta$, let $\preccurlyeq$ be the preorder induced by $\delta$, and for a noninvertible $r\in R$ let $V_r$ denote the highest power of $r$ dividing an element and $\mathbin{\cdot_r}$ the multiplication relation restricted according to powers of $r$. For multiplicati... | Can one characterize the subsets of R definable both in (R,+,-,0, multiplication, V_r, dot_r) and in (R,+,-,0, multiplication, V_s, dot_s) for multiplicatively independent non-invertible r and s? Is the corresponding structure F_0, the substructure of F_p[[X]] consisting of power series algebraic over F_p(X), decidable... | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,257 | OWR-15170-024 | Integer Predicates in Models of Totally Real Algebraic Integers | Let $(A,Z)$ be a ring of totally real algebraic integers with $Z$ named, and let $(R,S')$ be a model of its theory. If $(R,S)$ is the associated ultrapower model, with $S$ interpreting $Z$, must $S'\subseteq S$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | open | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-024",
"literature-status:open",
"owr-year:2016"
] | Conjecture S'\subseteq S remains unresolved; the source explicitly records that no further implication was known. | [
{
"url": "https://ems.press/content/serial-article-files/46652",
"label": "Oberwolfach Reports 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | Let $(A,Z)$ be a ring of totally real algebraic integers with $Z$ named, and let $(R,S')$ be a model of its theory. If $(R,S)$ is the associated ultrapower model, with $S$ interpreting $Z$, must $S'\subseteq S$? | Let (A,Z) be a ring of totally real algebraic integers with Z named, and let (R,S') be a model of its theory. Is the conjecture S' subseteq S valid when (R,S) is the corresponding ultrapower model with S the interpreted copy of Z? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,258 | OWR-15170-025 | Composite of Unrelated Field-Theory Questions | Can the valuation ring C[t]_(t) be defined diophantinely in C(t), and is the place f|_{s=0}|_{t=0}=0 diophantine in C(s,t) or in F_p(s,t)? Is there an infinite finitely axiomatizable field? For a valuation on an elementary extension Q* of Q as in the report, is the henselization necessarily separably closed? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | open | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official problem-session list shows that this extraction concatenates several unrelated questions about definable valuations, finitely a) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-025",
"literature-status:open",
"owr-year:2016"
] | The extracted record combines several open definability and finite-axiomatizability questions; current literature still identifies the infinite finitely axiomatizable field problem as open. | [
{
"url": "https://www.cambridge.org/core/journals/journal-of-symbolic-logic/article/finite-undecidability-in-nip-fields/FD28F4C52FA9926B68BF4278DDEE2751",
"label": "Finite undecidability in NIP fields"
},
{
"url": "https://ems.press/content/serial-article-files/46652",
"label": "Oberwolfach Repo... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | null | Can the valuation ring C[t]_(t) be defined diophantinely in C(t), and is the place f|_{s=0}|_{t=0}=0 diophantine in C(s,t) or in F_p(s,t)? Is there an infinite finitely axiomatizable field? For a valuation on an elementary extension Q* of Q as in the report, is the henselization necessarily separably closed? | unrecoverable | The official problem-session list shows that this extraction concatenates several unrelated questions about definable valuations, finitely axiomatizable fields, and henselizations. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,259 | OWR-15170-026 | Degree Definability and Existential Theory of Rational Function Fields | Is the relation $E$ on $\mathbb C[t]$, defined by $E(f,g)$ if and only if $\deg(f)=\deg(g)$, Diophantine or definable in the ring language with parameters? For a fixed prime $p$, is the existential theory of $\mathbb F_p(t)$ in the ring language decidable? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | open | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-026",
"literature-status:open",
"owr-year:2016"
] | The existential theory of F_p(t) in the pure ring language remains open; decidability results with a named parameter do not resolve the parameter-free question. | [
{
"url": "https://ems.press/content/serial-article-files/46652",
"label": "Oberwolfach Reports 2017"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | Is the relation $E$ on $\mathbb C[t]$, defined by $E(f,g)$ if and only if $\deg(f)=\deg(g)$, Diophantine or definable in the ring language with parameters? For a fixed prime $p$, is the existential theory of $\mathbb F_p(t)$ in the ring language decidable? | Is the degree-equivalence relation E on C[t], defined by E(f,g) iff deg(f)=deg(g), diophantine or definable in the ring language with parameters? For a fixed prime p, is the existential theory of F_p(t) in the ring language decidable? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,260 | OWR-15170-027 | Diophantine Definability of Rational Subfields | For the relation $S$ on $\mathbb F_p(t)$ defined by $S(f,g)$ if and only if $f\in\mathbb F_p(g)$, is $S$ Diophantine in the parameter-free ring language? In particular, is $\mathbb F_p(t^2)$ Diophantine with parameters in $\mathbb F_p(t)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | open | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-027",
"literature-status:open",
"owr-year:2016"
] | The report poses this Diophantine definability question for the relation S on F_p(t); no unconditional resolution was found in the subsequent literature checked. | [
{
"url": "https://doi.org/10.4171/owr/2016/49",
"label": "OWR 49 report"
},
{
"url": "https://ems.press/content/serial-article-files/46652",
"label": "EMS report text"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | For the relation $S$ on $\mathbb F_p(t)$ defined by $S(f,g)$ if and only if $f\in\mathbb F_p(g)$, is $S$ Diophantine in the parameter-free ring language? In particular, is $\mathbb F_p(t^2)$ Diophantine with parameters in $\mathbb F_p(t)$? | For the binary relation S on F_p(t) defined by S(f,g) iff f belongs to F_p(g), is S diophantine in the parameter-free ring language? In particular, is F_p(t^2) diophantine with parameters in F_p(t)? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,261 | OWR-15170-028 | Composite of Unrelated Decidability Questions | For an algebraically closed complete valued field k, determine whether the existential theory of the rigid entire-function ring A_k with t named is decidable in each of the archimedean, non-archimedean characteristic-zero, and non-archimedean positive-characteristic cases; likewise determine whether the theory of the r... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866](https://doi.org/10.4171/owr/2016/49)
## Literature review (che... | 3 | partially_solved | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Unrecoverable OWR statement (The official problem-session list shows that this extraction joins the decidability problem for rigid analytic function rings to a separate ) | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15170-028",
"literature-status:partially-solved",
"owr-year:2016"
] | The record bundles several theories: undecidability is known in several listed cases, while pure ring theories and other cases remain open; the 2023 p-adic result uses a richer valued-field language and does not settle the pure-ring questions. | [
{
"url": "https://doi.org/10.4171/owr/2016/49",
"label": "OWR 49 report"
},
{
"url": "https://doi.org/10.1016/j.apal.2022.103203",
"label": "Kartas 2023"
},
{
"url": "https://arxiv.org/abs/1501.04522",
"label": "Fehm 2015"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/49 | null | null | null | null | For an algebraically closed complete valued field k, determine whether the existential theory of the rigid entire-function ring A_k with t named is decidable in each of the archimedean, non-archimedean characteristic-zero, and non-archimedean positive-characteristic cases; likewise determine whether the theory of the r... | unrecoverable | The official problem-session list shows that this extraction joins the decidability problem for rigid analytic function rings to a separate question about totally real analogues over p-adic fields. No separate clean statement is promoted, and the original record remains publicly visible for provenance. | null | null | null | null | null | Definability and Decidability Problems in Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/49, pp. 2793--2866 |
30,003,262 | OWR-15172-001 | Analytical Foundations of Magnetoelastic Material Models | For mathematical models of magnetoelastic materials, what is the role of the saturation constraint; how can models of physical effects on different length scales be reconciled; what dissipation models are reasonable and derivable microscopically; do energy functionals admit minimizers; can hysteresis and nucleation be ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematics of Magnetoelastic Materials (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/51, pp. 2909--2940](https://doi.org/10.4171/owr/2016/51)
## Literature review (chec... | 3 | partially_solved | null | 2,016 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15172-001",
"literature-status:partially-solved",
"owr-year:2016"
] | The broad six-part agenda remains open, but rigorous existence of minimizers and quasistatic evolutions has been proved under important coercivity and saturation hypotheses. | [
{
"url": "https://doi.org/10.4171/owr/2016/51",
"label": "OWR 51 report"
},
{
"url": "https://doi.org/10.1007/s00526-023-02521-7",
"label": "Bresciani 2023"
},
{
"url": "https://doi.org/10.1137/S0036141004442021",
"label": "Rybka and Luskin 2005"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/51 | null | null | null | For mathematical models of magnetoelastic materials, what is the role of the saturation constraint; how can models of physical effects on different length scales be reconciled; what dissipation models are reasonable and derivable microscopically; do energy functionals admit minimizers; can hysteresis and nucleation be ... | For mathematical models of magnetoelastic materials, what is the role of the saturation constraint; how can models of physical effects on different length scales be reconciled; what dissipation models are reasonable and derivable microscopically; do energy functionals admit minimizers; can hysteresis and nucleation be ... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Mathematics of Magnetoelastic Materials (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/51, pp. 2909--2940 |
30,003,263 | OWR-15172-002 | Macroscopic Limits and Phase Diagrams of Ferroelectric Models | Do macroscopic polarization models for ferroelectric solids arise as the large-body limit of microscopic electron-density models, including the still-open lower-bound direction? Can one also systematically analyze the proposed random-field-Ising-like model with long-range interactions for the phase diagram of lead tita... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Mathematics of Magnetoelastic Materials (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/51, pp. 2909--2940](https://doi.org/10.4171/owr/2016/51)
## Literature review (chec... | 3 | open | null | 2,016 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15172-002",
"literature-status:open",
"owr-year:2016"
] | The cited work supplies an upper bound and numerical evidence, but explicitly leaves the lower bound and systematic analysis of the proposed long-range random-field model unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2016/51",
"label": "OWR 51 report"
},
{
"url": "https://ems.press/content/serial-article-files/46654?nt=1",
"label": "EMS report text"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/51 | null | null | null | Do macroscopic polarization models for ferroelectric solids arise as the large-body limit of microscopic electron-density models, including the still-open lower-bound direction? Can one also systematically analyze the proposed random-field-Ising-like model with long-range interactions for the phase diagram of lead tita... | Do macroscopic polarization models for ferroelectric solids arise as the large-body limit of microscopic electron-density models, including the still-open lower-bound direction? In addition, can one systematically analyze the proposed random-field-Ising-like model with long-range interactions for the phase diagram of l... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Mini-Workshop: Mathematics of Magnetoelastic Materials (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/51, pp. 2909--2940 |
30,003,264 | OWR-15173-001 | Third Homology and Pre-Bloch Groups of $S$-Arithmetic $\operatorname{SL}_2$ | For a global field $F$ and every sufficiently large finite set $S$ of places, is the natural map
$$\pi_S:\ker\!\left(H_3(\operatorname{SL}_2(\mathcal O_S),\mathbb Z[1/2])\to H_3(\operatorname{SL}_2(F),\mathbb Z[1/2])\right)\longrightarrow\bigoplus_{v\in S\setminus S_\infty}\mathcal P(k(v))\otimes\mathbb Z[1/2]$$
an i... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Computations in the Cohomology of Arithmetic Groups (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/52, pp. 2941--2973](https://doi.org/10.4171/owr/2016/52)
## Literature ... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15173-001",
"literature-status:open",
"owr-year:2016"
] | The report asks whether the map pi_S is eventually an isomorphism, and no authoritative later source located here proves or disproves that assertion. | [
{
"url": "https://doi.org/10.4171/owr/2016/52",
"label": "OWR 52 report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/52 | null | null | null | For a global field $F$ and every sufficiently large finite set $S$ of places, is the natural map
$$\pi_S:\ker\!\left(H_3(\operatorname{SL}_2(\mathcal O_S),\mathbb Z[1/2])\to H_3(\operatorname{SL}_2(F),\mathbb Z[1/2])\right)\longrightarrow\bigoplus_{v\in S\setminus S_\infty}\mathcal P(k(v))\otimes\mathbb Z[1/2]$$
an i... | For a global field F and sufficiently large finite sets S of places, is the natural map pi_S from the kernel of H_3(SL_2(O_S),Z[1/2]) to the direct sum over v in S\setminus S_infty of P(k(v)) tensor Z[1/2] an isomorphism? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Computations in the Cohomology of Arithmetic Groups (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/52, pp. 2941--2973 |
30,003,265 | OWR-15173-002 | Cuspidal Homology for Gaussian Bianchi Congruence Groups | Does there exist a prime $p\equiv5\pmod 8$ such that, writing $p=\mathfrak p\overline{\mathfrak p}$ in $\mathbb Z[i]$ and $\Gamma_0(\mathfrak p)\leq\operatorname{SL}_2(\mathbb Z[i])$, the group $H_1(\Gamma_0(\mathfrak p)\backslash\mathbb H^3;\mathbb Z)$ contains cuspidal classes? Or can one prove that no such prime exi... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Computations in the Cohomology of Arithmetic Groups (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/52, pp. 2941--2973](https://doi.org/10.4171/owr/2016/52)
## Literature ... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | false | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | Answered in the source or not an open problem () | null | null | [Discussion #4 literature review, 2026-09-29] . The record copies the source faithfully; the inconsistency is in the report itself. | [
"owr",
"oberwolfach-reports",
"OWR-15173-002",
"literature-status:open",
"owr-year:2016"
] | The computation reported no cuspidal class for p less than 16000, but no proof of nonexistence for all eligible primes or example beyond the search range was found. | [
{
"url": "https://orbilu.uni.lu/bitstream/10993/29499/1/preliminary_OWR_2016_52.pdf",
"label": "OWR 52 preliminary report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/52 | null | null | null | Does there exist a prime $p\equiv5\pmod 8$ such that, writing $p=\mathfrak p\overline{\mathfrak p}$ in $\mathbb Z[i]$ and $\Gamma_0(\mathfrak p)\leq\operatorname{SL}_2(\mathbb Z[i])$, the group $H_1(\Gamma_0(\mathfrak p)\backslash\mathbb H^3;\mathbb Z)$ contains cuspidal classes? Or can one prove that no such prime exi... | Does there exist a prime p congruent to 5 modulo 8 such that H_1(Gamma_0(mathfrak p)\backslash H^3;Z) contains cuspidal classes, for Gamma=SL_2(Z[i]) and p=mathfrak p\overline{mathfrak p}? Or can it be proved that no such prime exists? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Computations in the Cohomology of Arithmetic Groups (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/52, pp. 2941--2973 |
30,003,266 | OWR-15173-003 | Computing Hecke Operators for Arithmetic-Group Cohomology | Can Hecke operators and their eigenvalues be computed for all arithmetic groups for which the cohomology can be calculated? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Computations in the Cohomology of Arithmetic Groups (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/52, pp. 2941--2973](https://doi.org/10.4171/owr/2016/52)
## Literature ... | 3 | partially_solved | null | 2,016 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15173-003",
"literature-status:partially-solved",
"owr-year:2016"
] | Algorithms now compute Hecke operators for broad GL_n arithmetic groups over number fields and division algebras, but the question for all arithmetic groups remains unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2016/52",
"label": "OWR 52 report"
},
{
"url": "https://arxiv.org/abs/2010.06036",
"label": "McConnell and MacPherson"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/52 | null | null | null | Can Hecke operators and their eigenvalues be computed for all arithmetic groups for which the cohomology can be calculated? | Can Hecke operators and their eigenvalues be computed for all arithmetic groups for which the cohomology can be calculated? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Computations in the Cohomology of Arithmetic Groups (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/52, pp. 2941--2973 |
30,003,267 | OWR-15173-004 | Subexponential Completeness Testing for Voronoi Cell Representatives | Given a Voronoi cell complex $\operatorname{Vor}_\Gamma$ and a proposed set $C_d$ of representatives of its $d$-cells modulo $\Gamma$, is there a subexponential-time algorithm for deciding whether $C_d$ is complete? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Computations in the Cohomology of Arithmetic Groups (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/52, pp. 2941--2973](https://doi.org/10.4171/owr/2016/52)
## Literature ... | 3 | open | null | 2,016 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15173-004",
"literature-status:open",
"owr-year:2016"
] | The report asks for a subexponential completeness test for representatives of Voronoi cells modulo the group; no general algorithm resolving this question was found. | [
{
"url": "https://orbilu.uni.lu/bitstream/10993/29499/1/preliminary_OWR_2016_52.pdf",
"label": "OWR 52 preliminary report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/52 | null | null | null | Given a Voronoi cell complex $\operatorname{Vor}_\Gamma$ and a proposed set $C_d$ of representatives of its $d$-cells modulo $\Gamma$, is there a subexponential-time algorithm for deciding whether $C_d$ is complete? | Given a Voronoi-type cell complex Vor_Gamma and the representatives C_d of its d-cells modulo Gamma, is there an algorithm that checks in subexponential runtime whether C_d is complete? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Computations in the Cohomology of Arithmetic Groups (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/52, pp. 2941--2973 |
30,003,268 | OWR-15173-005 | Discrete Vector Fields for Voronoi-Cohomology Computations | Can the discrete vector-field technique be applied effectively to cohomological computations with the Voronoi cell complex? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Computations in the Cohomology of Arithmetic Groups (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/52, pp. 2941--2973](https://doi.org/10.4171/owr/2016/52)
## Literature ... | 3 | open | null | 2,016 | 15 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 15,
"name": "computer_science",
"display_name": "Computer Science",
"description": "Computational complexity, algorithms, and theoretical CS.",
"slug": "computer-science",
"order_index": 15,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15173-005",
"literature-status:open",
"owr-year:2016"
] | The proposed use of discrete vector fields for cohomology computations on Voronoi cell complexes remains an explicitly unresolved methodological question. | [
{
"url": "https://orbilu.uni.lu/bitstream/10993/29499/1/preliminary_OWR_2016_52.pdf",
"label": "OWR 52 preliminary report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/52 | null | null | null | Can the discrete vector-field technique be applied effectively to cohomological computations with the Voronoi cell complex? | Can the discrete vector-field technique be applied effectively to cohomological computations with the Voronoi cell complex? | exact | The supplied statement is clear, self-contained, and publication-ready and is retained byte-for-byte. | null | null | null | null | null | Mini-Workshop: Computations in the Cohomology of Arithmetic Groups (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/52, pp. 2941--2973 |
30,003,269 | OWR-15173-006 | Fields of Definition of Eutactic Forms | Can one predict the field of definition of a eutactic form over $\mathbb Q$ or another number field? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Computations in the Cohomology of Arithmetic Groups (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/52, pp. 2941--2973](https://doi.org/10.4171/owr/2016/52)
## Literature ... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15173-006",
"literature-status:open",
"owr-year:2016"
] | The field-of-definition question for eutactic lattices remains open; current problem surveys still ask whether every number field with a real place can occur. | [
{
"url": "https://jamartin.perso.math.cnrs.fr/problat.pdf",
"label": "Martinet problem survey"
},
{
"url": "https://www.ams.org/journals/bull/2004-41-04/S0273-0979-04-01018-3/S0273-0979-04-01018-3.pdf",
"label": "AMS lattice survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/52 | null | null | null | Can one predict the field of definition of a eutactic form over $\mathbb Q$ or another number field? | Can one predict the field of definition of a eutactic form over Q or over another number field? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Computations in the Cohomology of Arithmetic Groups (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/52, pp. 2941--2973 |
30,003,270 | OWR-15173-007 | Explicit Reduction Theory for Rank-One Unitary Arithmetic Groups | Let $L=\mathbb Q(\sqrt{-d})$ with $d>0$ square-free, let
$$G(\mathbb Q)=\{g\in\operatorname{SL}_3(L):g^*Jg=J\}$$
be a $\mathbb Q$-rank-one unitary group, and let $\Gamma\leq G(\mathbb Q)$ be an arithmetic subgroup. Can one carry out explicit reduction theory for $\Gamma$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Computations in the Cohomology of Arithmetic Groups (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/52, pp. 2941--2973](https://doi.org/10.4171/owr/2016/52)
## Literature ... | 3 | open | null | 2,016 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15173-007",
"literature-status:open",
"owr-year:2016"
] | Explicit reduction is known in some related unitary examples, but no general explicit reduction theory for the unitary groups posed in the report was found. | [
{
"url": "https://doi.org/10.4171/owr/2016/52",
"label": "OWR 52 report"
},
{
"url": "https://arxiv.org/abs/math/0601071",
"label": "Yasaki related reduction"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/52 | null | null | null | Let $L=\mathbb Q(\sqrt{-d})$ with $d>0$ square-free, let
$$G(\mathbb Q)=\{g\in\operatorname{SL}_3(L):g^*Jg=J\}$$
be a $\mathbb Q$-rank-one unitary group, and let $\Gamma\leq G(\mathbb Q)$ be an arithmetic subgroup. Can one carry out explicit reduction theory for $\Gamma$? | For a Q-rank-one form of SL_3 and a subgroup Gamma of G(Q)={g in SL_3(L):g^*Jg=J}, where L=Q(sqrt(d)) and d is square-free positive, can one carry out explicit reduction theory for Gamma? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Mini-Workshop: Computations in the Cohomology of Arithmetic Groups (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/52, pp. 2941--2973 |
30,003,271 | OWR-15174-002 | Squarefree Group Orders in Elliptic-Curve Reductions | Let $E/\mathbb Q$ be an elliptic curve with $\operatorname{End}_{\mathbb Q}(E)\cong\mathbb Z$. Does there exist an explicit constant $\delta(E)$ such that
$$\#\{p\leq x:\#E(\mathbb F_p)\text{ is square-free}\}\sim\delta(E)\pi(x)$$
as $x\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030](https://doi.org/10.4171/owr/2016/53)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15174-002",
"literature-status:open",
"owr-year:2016"
] | The squarefree-order conjecture is supported by average results and has advances in the CM case, but the stated non-CM case End_Q(E) equal to Z remains open. | [
{
"url": "https://oa.tib.eu/renate/bitstreams/7113322d-c5e3-40f5-817e-0d93cf4769d3/download",
"label": "OWR 53 report text"
},
{
"url": "https://arxiv.org/abs/2408.05904",
"label": "Wong 2024"
},
{
"url": "https://doi.org/10.1090/spmj/1483",
"label": "Zarhin 2024"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/53 | null | null | null | Let $E/\mathbb Q$ be an elliptic curve with $\operatorname{End}_{\mathbb Q}(E)\cong\mathbb Z$. Does there exist an explicit constant $\delta(E)$ such that
$$\#\{p\leq x:\#E(\mathbb F_p)\text{ is square-free}\}\sim\delta(E)\pi(x)$$
as $x\to\infty$? | For an elliptic curve E over Q with End_Q(E) isomorphic to Z, does there exist an explicit constant delta(E) such that the number of primes p up to x for which E_p(F_p) has squarefree order is asymptotic to delta(E) pi(x)? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030 |
30,003,272 | OWR-15174-003 | Zeta Moments from Shifted Divisor Correlations | How can the conjectured $2k$th moments of the Riemann zeta function be derived arithmetically from shifted-divisor problems, including the required $k$-fold convolutions of shifted divisor sums? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030](https://doi.org/10.4171/owr/2016/53)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15174-003",
"literature-status:open",
"owr-year:2016"
] | The shifted-divisor approach gives substantial moment heuristics and finite-order results, but a derivation of the full Riemann-zeta moment conjectures remains unresolved. | [
{
"url": "https://ems.press/content/serial-article-files/46657?nt=1",
"label": "OWR 53 report text"
},
{
"url": "https://doi.org/10.1098/rsta.2014.0313",
"label": "Conrey and Keating"
},
{
"url": "https://arxiv.org/abs/1506.06842",
"label": "Moments survey"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/53 | null | null | null | How can the conjectured $2k$th moments of the Riemann zeta function be derived arithmetically from shifted-divisor problems, including the required $k$-fold convolutions of shifted divisor sums? | How can the conjectured moments of the Riemann zeta function be obtained from shifted-divisor problems, including the required k-fold convolutions of shifted divisor sums? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030 |
30,003,273 | OWR-15174-004 | Moments of Quadratic Dirichlet L-Functions over Function Fields | Fix $q\equiv1\pmod 4$, and let $\mathcal H_{2g+1}$ be the set of monic square-free polynomials of degree $2g+1$ over $\mathbb F_q$. For fixed $k$, does
$$\sum_{D\in\mathcal H_{2g+1}}L(1/2,\chi_D)^k=q^{2g+1}P_k(2g+1)+o(q^{2g+1})$$
hold as $g\to\infty$, where $P_k$ has degree $k(k+1)/2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030](https://doi.org/10.4171/owr/2016/53)
## Literature review (checked 2026-08-21)
**Status:** par... | 3 | partially_solved | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15174-004",
"literature-status:partially-solved",
"owr-year:2016"
] | The Andrade--Keating function-field moment conjecture has proved leading terms and expected-order results for several moments, including the fourth, but the full polynomial asymptotic for every fixed k remains open. | [
{
"url": "https://doi.org/10.1016/j.jnt.2014.02.019",
"label": "Andrade and Keating"
},
{
"url": "https://doi.org/10.1007/s00039-017-0409-8",
"label": "Florea 2017"
},
{
"url": "https://doi.org/10.1016/j.ffa.2022.102113",
"label": "Function-field moments 2022"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/53 | null | null | null | Fix $q\equiv1\pmod 4$, and let $\mathcal H_{2g+1}$ be the set of monic square-free polynomials of degree $2g+1$ over $\mathbb F_q$. For fixed $k$, does
$$\sum_{D\in\mathcal H_{2g+1}}L(1/2,\chi_D)^k=q^{2g+1}P_k(2g+1)+o(q^{2g+1})$$
hold as $g\to\infty$, where $P_k$ has degree $k(k+1)/2$? | For fixed q congruent to 1 modulo 4 and the family H_{2g+1} of monic square-free polynomials of degree 2g+1 over F_q, does the conjectured asymptotic formula sum_{D in H_{2g+1}} L(1/2,chi_D)^k = q^{2g+1}P_k(2g+1)+o(1) hold as g tends to infinity, with P_k of degree k(k+1)/2? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030 |
30,003,274 | OWR-15174-006 | Preperiods and Cycles of Quadratic Polynomial Iteration | For a quadratic polynomial $f\in\mathbb F_q[x]$ and $m\in\mathbb F_q$, determine the preperiod and eventual period of the orbit $m,f(m),f^{\circ2}(m),\ldots$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030](https://doi.org/10.4171/owr/2016/53)
## Literature review (checked 2026-08-21)
**Status:** par... | 3 | partially_solved | null | 2,016 | 11 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 11,
"name": "dynamical_systems",
"display_name": "Dynamical Systems",
"description": "Problems about long-term behavior of deterministic systems, Hamiltonian dynamics, and periodic orbits.",
"slug": "dynamical-systems",
"order_index": 11,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15174-006",
"literature-status:partially-solved",
"owr-year:2016"
] | Heath-Brown proved strong cycle-length bounds and analyzed important quadratic families, but the exact cycle length for a general quadratic polynomial over a finite field is not determined. | [
{
"url": "https://doi.org/10.1112/S0025579317000328",
"label": "Heath-Brown 2017"
},
{
"url": "https://arxiv.org/abs/1701.02707",
"label": "Heath-Brown preprint"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/53 | null | null | null | For a quadratic polynomial $f\in\mathbb F_q[x]$ and $m\in\mathbb F_q$, determine the preperiod and eventual period of the orbit $m,f(m),f^{\circ2}(m),\ldots$. | For a quadratic polynomial f over F_q and an initial value m, how long does the iteration sequence f_0(m),f_1(m),f_2(m),... take to enter its eventual cycle, and how long is that cycle? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030 |
30,003,275 | OWR-15174-007 | Distribution of Minimal Rational-Point Heights on Fano Intersections | For smooth Fano complete intersections $V/\mathbb Q$ parametrized by $\mathcal V_{d,n}$, let $H(V)$ be the parameter height and $M(V)$ the least height of a rational point. For $0<t<1$, is
$$\limsup_{A\to\infty}\frac{\#\{V\in\mathcal V_{d,n}:H(V)\leq A,\ M(V)\leq tH(V)\}}{\#\{V\in\mathcal V_{d,n}:H(V)\leq A\}}=O(t)$$
... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030](https://doi.org/10.4171/owr/2016/53)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15174-007",
"literature-status:open",
"owr-year:2016"
] | The extracted conjecture is incomplete, and existing statistical results for smallest rational points on random Fano varieties do not establish the general height-distribution claim. | [
{
"url": "https://doi.org/10.4171/owr/2016/53",
"label": "OWR 53 report"
},
{
"url": "https://doi.org/10.2140/ant.2021.15.657",
"label": "Le Boudec 2021"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/53 | null | null | null | For smooth Fano complete intersections $V/\mathbb Q$ parametrized by $\mathcal V_{d,n}$, let $H(V)$ be the parameter height and $M(V)$ the least height of a rational point. For $0<t<1$, is
$$\limsup_{A\to\infty}\frac{\#\{V\in\mathcal V_{d,n}:H(V)\leq A,\ M(V)\leq tH(V)\}}{\#\{V\in\mathcal V_{d,n}:H(V)\leq A\}}=O(t)$$
... | For the family of smooth Fano complete intersections V over Q parametrized by V_{d,n}, does the proportion of varieties of height at most A having lowest rational-point height M(V) at most t H(V) remain O(t) as A tends to infinity, for 0<t<1? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030 |
30,003,276 | OWR-15174-008 | Brauer–Manin Sufficiency for Smooth Fano Hypersurfaces | For smooth Fano hypersurfaces, is the Brauer–Manin obstruction the only obstruction to the Hasse principle, as predicted by the Colliot-Thélène conjecture? Equivalently in the source's density formulation, is $\delta_{\mathrm{global}}=\delta_{\mathrm{local}}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030](https://doi.org/10.4171/owr/2016/53)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15174-008",
"literature-status:open",
"owr-year:2016"
] | The general Colliot--Thélène conjecture invoked by the record remains unresolved, despite strong almost-all results for random Fano hypersurfaces. | [
{
"url": "https://doi.org/10.4171/owr/2016/53",
"label": "OWR 53 report"
},
{
"url": "https://doi.org/10.4007/annals.2023.197.3.3",
"label": "Browning, Le Boudec, and Sawin"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/53 | null | null | null | For smooth Fano hypersurfaces, is the Brauer–Manin obstruction the only obstruction to the Hasse principle, as predicted by the Colliot-Thélène conjecture? Equivalently in the source's density formulation, is $\delta_{\mathrm{global}}=\delta_{\mathrm{local}}$? | Is the Colliot-Thelene conjecture true that, for smooth Fano hypersurfaces, the Brauer-Manin obstruction is the only obstruction to the Hasse principle, and hence that delta global equals delta local? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030 |
30,003,277 | OWR-15174-010 | Three Problems from an Analytic Number Theory Session | Does there exist a Dirichlet series $D(s)$ that converges in a half-plane $\operatorname{Re}s>\alpha$ and has exactly one zero there? For the ordered Laplace eigenvalues $0<\lambda_1\leq\lambda_2\leq\cdots$ of Maass forms on $\operatorname{SL}_2(\mathbb Z)\backslash\mathbb H$, are
$$\liminf_{j\to\infty}(\lambda_{j+1}-... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030](https://doi.org/10.4171/owr/2016/53)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15174-010",
"literature-status:open",
"owr-year:2016"
] | The proposed Dirichlet series construction is not established: the later Hilberdink--Saias preprint was withdrawn because of an unrepairable error in its main proof. | [
{
"url": "https://doi.org/10.4171/owr/2016/53",
"label": "OWR 53 report"
},
{
"url": "https://arxiv.org/abs/1812.11880",
"label": "Withdrawn Hilberdink--Saias preprint"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/53 | null | null | null | Does there exist a Dirichlet series $D(s)$ that converges in a half-plane $\operatorname{Re}s>\alpha$ and has exactly one zero there? For the ordered Laplace eigenvalues $0<\lambda_1\leq\lambda_2\leq\cdots$ of Maass forms on $\operatorname{SL}_2(\mathbb Z)\backslash\mathbb H$, are
$$\liminf_{j\to\infty}(\lambda_{j+1}-... | Does there exist an unconditional Dirichlet series D(s) converging in a half-plane sigma greater than alpha with exactly one zero there; for Maass-form eigenvalues 0 less than lambda_1 less than or equal to lambda_2 less than or equal to dots, can one prove that the liminf of lambda_{j+1}-lambda_j is 0 and the limsup i... | corrected_verified | The official problem-session report was checked. The two clauses duplicated in OWR-15174-011 were removed, leaving the three distinct source questions in this record. | null | null | null | null | null | Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030 |
30,003,278 | OWR-15174-011 | Elliptic-Curve Bijections and Additive Bases from Restricted Primes | Let $p>3$, let $t\not\equiv0\pmod p$, and put
$$E_p(t)=\{(x,y)\in(\mathbb F_p^\times)^2:x+x^{-1}+y+y^{-1}=t\}.$$
Is there an explicit bijection $E_p(t)\to E_p(16/t)$? Also, if $S$ is the set of positive integers all of whose prime divisors are congruent to $3$ modulo $4$, is every sufficiently large even integer a su... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030](https://doi.org/10.4171/owr/2016/53)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15174-011",
"literature-status:open",
"owr-year:2016"
] | The record combines a finite-field point-count identity with the separate assertion that every sufficiently large even number is a sum of two members of S; the latter remains unresolved, so the extracted composite record is open. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3557/OWR_2016_53.pdf?isAllowed=y&sequence=1",
"label": "OWR 53 report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/53 | null | null | null | Let $p>3$, let $t\not\equiv0\pmod p$, and put
$$E_p(t)=\{(x,y)\in(\mathbb F_p^\times)^2:x+x^{-1}+y+y^{-1}=t\}.$$
Is there an explicit bijection $E_p(t)\to E_p(16/t)$? Also, if $S$ is the set of positive integers all of whose prime divisors are congruent to $3$ modulo $4$, is every sufficiently large even integer a su... | For p greater than 3 and t nonzero modulo p, does there exist a bijective proof mapping points of E_p(t), defined by x plus 1 over x plus y plus 1 over y equals t modulo p, to E_p(16/t); and is every sufficiently large even integer a sum of two members of S equals the set of natural numbers whose prime divisors are all... | corrected_verified | The official problem-session report was checked. This record retains the two source questions omitted from the overlapping composite extraction OWR-15174-010. | null | null | null | null | null | Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030 |
30,003,279 | OWR-15174-012 | Minimal Separations Among Lattice Points on Circles | Let $n$ be a product of distinct primes congruent to $1$ modulo $4$, and consider the lattice points on $x^2+y^2=n$. Can three such points attain separation of order $R^{1/3}$, where $R=\sqrt n$, and how small can the separation be for configurations of $k$ such points? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030](https://doi.org/10.4171/owr/2016/53)
## Literature review (checked 2026-08-21)
**Status:** par... | 3 | partially_solved | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15174-012",
"literature-status:partially-solved",
"owr-year:2016"
] | The two-, three-, and four-point questions have substantial results, including sharp constructions for four close lattice points, but the broader close-cluster questions remain open. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3557/OWR_2016_53.pdf?isAllowed=y&sequence=1",
"label": "OWR 53 report"
},
{
"url": "https://doi.org/10.4153/CJM-2009-057-2",
"label": "Cilleruelo and Granville"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/53 | null | null | null | Let $n$ be a product of distinct primes congruent to $1$ modulo $4$, and consider the lattice points on $x^2+y^2=n$. Can three such points attain separation of order $R^{1/3}$, where $R=\sqrt n$, and how small can the separation be for configurations of $k$ such points? | Let n be a product of distinct primes congruent to 1 modulo 4, and consider the lattice points on x^2 plus y^2 equals n. Can three such points, or more generally configurations with k points, attain the known lower-bound separations, including the order R^{1/3} bound for three points? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030 |
30,003,280 | OWR-15174-014 | Euclid-Type Expressions for Primes Congruent to Three Modulo Four | Let $p_1<p_2<\cdots$ be all primes and $q_1<q_2<\cdots$ the primes congruent to $3$ modulo $4$. Writing $P_k=\prod_{i=1}^kp_i$ and $Q_k=\prod_{i=1}^kq_i$, can one construct a Euclid-type expression in $Q_k$ whose least prime divisor is $q_{k+1}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030](https://doi.org/10.4171/owr/2016/53)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15174-014",
"literature-status:open",
"owr-year:2016"
] | The proposed expression with least prime divisor q_{k+1} is an unresolved problem; no authoritative later construction or impossibility proof was found. | [
{
"url": "https://publications.mfo.de/bitstream/handle/mfo/3557/OWR_2016_53.pdf?isAllowed=y&sequence=1",
"label": "OWR 53 report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/53 | null | null | null | Let $p_1<p_2<\cdots$ be all primes and $q_1<q_2<\cdots$ the primes congruent to $3$ modulo $4$. Writing $P_k=\prod_{i=1}^kp_i$ and $Q_k=\prod_{i=1}^kq_i$, can one construct a Euclid-type expression in $Q_k$ whose least prime divisor is $q_{k+1}$? | If p_1 less than p_2 less than dots are all primes, q_1 less than q_2 less than dots are the primes congruent to 3 modulo 4, and P and Q are the products of the first k respective primes, can one define an expression in Q whose least prime divisor is q_{k+1}? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030 |
30,003,281 | OWR-15174-015 | Abundance of Zeros in Families of Quadratic Forms | Fix integral quadratic polynomials $Q_1,\ldots,Q_h$ in $t$ variables. For coefficient vectors $\mathbf x=(x_1,\ldots,x_h)$ with $\lvert x_i\rvert\leq B^\theta$, is it true for a positive proportion of $\mathbf x$ that
$$\#\{\mathbf y\in\mathbb Z^t:\lvert y_j\rvert\leq B,\ \textstyle\sum_{i=1}^h x_iQ_i(\mathbf y)=0\}\g... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030](https://doi.org/10.4171/owr/2016/53)
## Literature review (checked 2026-08-21)
**Status:** ope... | 3 | open | null | 2,016 | 1 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 1,
"name": "number_theory",
"display_name": "Number Theory",
"description": "Properties of integers, prime numbers, Diophantine equations.",
"slug": "number-theory",
"order_index": 1,
"created_at": "2026-07-31T15:26:25.670Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15174-015",
"literature-status:open",
"owr-year:2016"
] | The requested positive-proportion estimate for quadratic polynomials in the stated range is posed in the source report, and no authoritative proof or disproof of this exact claim was found. | [
{
"url": "https://doi.org/10.4171/owr/2016/53",
"label": "Oberwolfach Report 53 (2016)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/53 | null | null | null | Fix integral quadratic polynomials $Q_1,\ldots,Q_h$ in $t$ variables. For coefficient vectors $\mathbf x=(x_1,\ldots,x_h)$ with $\lvert x_i\rvert\leq B^\theta$, is it true for a positive proportion of $\mathbf x$ that
$$\#\{\mathbf y\in\mathbb Z^t:\lvert y_j\rvert\leq B,\ \textstyle\sum_{i=1}^h x_iQ_i(\mathbf y)=0\}\g... | For fixed integral quadratic polynomials Q_1 through Q_h and fixed integers x_i with absolute value at most B^theta, is it true for a positive proportion of the coefficient vectors x that the number of integer y with absolute values at most B satisfying x_1Q_1(y) plus dots plus x_hQ_h(y) equals 0 is at least a constant... | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Analytic Number Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/53, pp. 2975--3030 |
30,003,282 | OWR-15175-003 | Hydrodynamic Limits for Non-Gradient Crystal-Lattice Systems | Can the hydrodynamic limit be derived for a non-gradient interacting particle system on a crystal lattice? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Large Scale Stochastic Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/54, pp. 3031--3086](https://doi.org/10.4171/owr/2016/54)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,016 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15175-003",
"literature-status:open",
"owr-year:2016"
] | Hydrodynamic limits are known for important periodic crystal-lattice models, but the general non-gradient crystal-lattice hydrodynamic limit identified in the record is not resolved. | [
{
"url": "https://arxiv.org/abs/2004.09158",
"label": "Guan crystal-lattice hydrodynamics"
},
{
"url": "https://doi.org/10.4171/owr/2016/54",
"label": "Oberwolfach Report 54 (2016)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/54 | null | null | null | Can the hydrodynamic limit be derived for a non-gradient interacting particle system on a crystal lattice? | Can the hydrodynamic limit be derived for a non-gradient interacting particle system on a crystal lattice? | exact | The statement is internally readable and complete; retained byte-for-byte. | null | null | null | null | null | Large Scale Stochastic Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/54, pp. 3031--3086 |
30,003,283 | OWR-15175-006 | Baik–Rains Fluctuations for General Stationary Exclusion Processes | Does the stationary exclusion-process current fluctuation limit with $T^{1/3}$ scaling and the Baik–Rains distribution, established for ASEP, continue to hold for general stationary exclusion processes with non-nearest-neighbor jumps? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Large Scale Stochastic Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/54, pp. 3031--3086](https://doi.org/10.4171/owr/2016/54)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,016 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15175-006",
"literature-status:open",
"owr-year:2016"
] | Aggarwal proves the stationary ASEP asymptotics, but the source explicitly leaves open whether the same statement holds for general stationary exclusion processes with non-nearest-neighbor jumps. | [
{
"url": "https://arxiv.org/abs/1608.04726",
"label": "Aggarwal stationary ASEP theorem"
},
{
"url": "https://doi.org/10.4171/owr/2016/54",
"label": "Oberwolfach Report 54 (2016)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/54 | null | null | null | Does the stationary exclusion-process current fluctuation limit with $T^{1/3}$ scaling and the Baik–Rains distribution, established for ASEP, continue to hold for general stationary exclusion processes with non-nearest-neighbor jumps? | Does the stationary exclusion-process current fluctuation limit with T^{1/3} scaling and the Baik-Rains distribution, established for ASEP, continue to hold for general stationary exclusion processes with non-nearest-neighbor jumps? | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Large Scale Stochastic Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/54, pp. 3031--3086 |
30,003,284 | OWR-15175-007 | Low-Vacancy Diffusion in Kinetically Constrained Lattice Gases | What is the correct asymptotic order of the diffusion coefficient $D(q)$ as the vacancy density $q$ tends to zero in kinetically constrained lattice-gas models? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Large Scale Stochastic Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/54, pp. 3031--3086](https://doi.org/10.4171/owr/2016/54)
## Literature review (checked 2026-08-21)
**Stat... | 3 | open | null | 2,016 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15175-007",
"literature-status:open",
"owr-year:2016"
] | Positive diffusion at every positive vacancy density is proved, but the correct asymptotic order of the diffusion coefficient as the vacancy density tends to zero remains undetermined. | [
{
"url": "https://arxiv.org/abs/1701.07663",
"label": "Blondel and Toninelli"
},
{
"url": "https://doi.org/10.4171/owr/2016/54",
"label": "Oberwolfach Report 54 (2016)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/54 | null | null | null | What is the correct asymptotic order of the diffusion coefficient $D(q)$ as the vacancy density $q$ tends to zero in kinetically constrained lattice-gas models? | What is the correct asymptotic order of the diffusion coefficient D(q) as q tends to 0 in the kinetically constrained lattice-gas models? | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Large Scale Stochastic Dynamics (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/54, pp. 3031--3086 |
30,003,285 | OWR-15176-001 | Return Probabilities and Stability of the Liouville Property | If a symmetric random walk with step distribution $\mu$ on a group $G$ satisfies $\mu^{(2n)}(e)\geq\exp(-cn^{1/2})$, must $(G,\mu)$ have the Liouville property? For a finitely generated group, is the Liouville property stable under changing the finite generating set? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Heat Kernels, Stochastic Processes and Functional Inequalities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/55, pp. 3087--3147](https://doi.org/10.4171/owr/2016/55)
## Literature revi... | 3 | open | null | 2,016 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15176-001",
"literature-status:open",
"owr-year:2016"
] | The sub-square-root return-probability threshold and stability of the Liouville property under changing generators are still stated as open; later work proves only the strict sub-threshold criterion. | [
{
"url": "https://doi.org/10.1093/imrn/rny034",
"label": "Peres and Zheng (2020)"
},
{
"url": "https://ems.press/content/serial-article-files/46659?nt=1",
"label": "Oberwolfach Report 55 (2016)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/55 | null | null | null | If a symmetric random walk with step distribution $\mu$ on a group $G$ satisfies $\mu^{(2n)}(e)\geq\exp(-cn^{1/2})$, must $(G,\mu)$ have the Liouville property? For a finitely generated group, is the Liouville property stable under changing the finite generating set? | For a symmetric random walk with return probability mu^{(2n)}(e) at least exp(-c n^{1/2}), does the pair (G,mu) necessarily have the Liouville property; and is the Liouville property stable under changing the generating set of a finitely generated group? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Heat Kernels, Stochastic Processes and Functional Inequalities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/55, pp. 3087--3147 |
30,003,286 | OWR-15176-003 | Processes Associated with Regular Representations of Dirichlet Forms | Let $(\mathcal E,W)$ be a Dirichlet form on $L^2(\mathbb R^d,\rho(x)\,dx)$, let $(\mathcal E,H)$ be its closed realization, and suppose a regular representation of $(\mathcal E,W)$ is given. Which stochastic process is associated with the regular representation, and how is it related to the process associated with $(\m... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Heat Kernels, Stochastic Processes and Functional Inequalities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/55, pp. 3087--3147](https://doi.org/10.4171/owr/2016/55)
## Literature revi... | 3 | open | null | 2,016 | 19 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 19,
"name": "probability",
"display_name": "Probability",
"description": "Problems involving probability theory, stochastic processes, and random structures.",
"slug": "probability",
"order_index": 19,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15176-003",
"literature-status:open",
"owr-year:2016"
] | Regular representations exist and concrete examples are understood, but a general description of the associated stochastic process and its relation to the original form remains unresolved. | [
{
"url": "https://doi.org/10.2969/jmsj/92649264",
"label": "Li (2025)"
},
{
"url": "https://ems.press/content/serial-article-files/46659?nt=1",
"label": "Oberwolfach Report 55 (2016)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/55 | null | null | null | Let $(\mathcal E,W)$ be a Dirichlet form on $L^2(\mathbb R^d,\rho(x)\,dx)$, let $(\mathcal E,H)$ be its closed realization, and suppose a regular representation of $(\mathcal E,W)$ is given. Which stochastic process is associated with the regular representation, and how is it related to the process associated with $(\m... | Given the Dirichlet form (E,W) on L^2(R^d,rho dx) and its regular representation, what stochastic process is associated with it, and how does that process relate to the one associated with (E,H) on the same space? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Heat Kernels, Stochastic Processes and Functional Inequalities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/55, pp. 3087--3147 |
30,003,287 | OWR-15176-004 | Metric-Tensor Scaling in Liouville Quantum Gravity | For $\gamma$-Liouville quantum gravity, is the scaling-limit metric tensor associated with the field $h$ given formally by
$$e^{2\gamma h/\beta}(dx^2+dy^2),$$
where $\beta$ is the Hausdorff dimension of the Liouville metric? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Heat Kernels, Stochastic Processes and Functional Inequalities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/55, pp. 3087--3147](https://doi.org/10.4171/owr/2016/55)
## Literature revi... | 3 | solved | null | 2,016 | 16 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 16,
"name": "physics",
"display_name": "Mathematical Physics",
"description": "Problems at the intersection of mathematics and physics.",
"slug": "physics",
"order_index": 16,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1007/s10240-020-00121-1",
"checked_at": "2026-09-30",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **solved (yes)**. C. Garban (OWR 55/2016, p. 3118) conjectures that the metric of γ-Liouville quantum gravity corresponds to the tensor e^{2γh/β}(dx² + dy²), with β the Hausdorff dimension of the metric, not to the naive e^{γh}(dx² + dy²). This is how the LQG metric is now ... | [
"owr",
"oberwolfach-reports",
"OWR-15176-004",
"literature-status:open",
"owr-year:2016"
] | The QLE metric has been constructed and its construction is distinct from a naive direct regularization, but the stated non-correspondence conjecture for the formal metric tensor has not been proved. | [
{
"url": "https://link.springer.com/article/10.1007/s00222-019-00905-1",
"label": "Miller and Sheffield QLE metric"
},
{
"url": "https://link.springer.com/article/10.1007/s00222-020-00991-6",
"label": "Gwynne, Miller, and Sheffield LQG metric"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/55 | null | null | null | For $\gamma$-Liouville quantum gravity, is the scaling-limit metric tensor associated with the field $h$ given formally by
$$e^{2\gamma h/\beta}(dx^2+dy^2),$$
where $\beta$ is the Hausdorff dimension of the Liouville metric? | For gamma-Liouville quantum gravity, is the metric tensor corresponding to the field h equal in the scaling limit to exp(2 gamma h divided by beta)(dx^2+dy^2), where beta is the Hausdorff dimension of the Liouville metric? | corrected_verified | The mathematical content was preserved while notation, typography, or omitted definitions were repaired for self-contained publication. | null | null | null | null | null | Heat Kernels, Stochastic Processes and Functional Inequalities (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/55, pp. 3087--3147 |
30,003,288 | OWR-15177-002 | Simplicial Volumes of Surface Bundles | For surface bundles with fixed closed fiber $F$ and base $B$, can the simplicial volume be bounded above in terms of the Euler characteristics, and are there finitely or infinitely many possible simplicial-volume values? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195](https://doi.org/10.4171/owr/2016/56)
## Literature review (checked 2026-08-21)
**Status:** open
**As... | 3 | open | null | 2,016 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15177-002",
"literature-status:open",
"owr-year:2016"
] | There are substantial bounds and special constructions for simplicial volumes, but no general theorem determines whether the set of values is finite or infinite for fixed fiber and base. | [
{
"url": "https://doi.org/10.4171/owr/2016/56",
"label": "Oberwolfach Report 56 (2017)"
},
{
"url": "https://doi.org/10.1007/s10711-020-00570-2",
"label": "Bucher and Campagnolo (2021)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/56 | null | null | null | For surface bundles with fixed closed fiber $F$ and base $B$, can the simplicial volume be bounded above in terms of the Euler characteristics, and are there finitely or infinitely many possible simplicial-volume values? | For surface bundles over fixed closed surfaces F and B, can the simplicial volume be bounded above in terms of the Euler characteristic, and are there finitely or infinitely many possible simplicial-volume values? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195 |
30,003,289 | OWR-15177-003 | Johnson-Filtration Images of Stable Heegaard Splittings | For the Johnson-filtration images $V_k(3)$ of stable Heegaard splittings of integral homology $3$-spheres, describe $V_k(3)$ and determine whether $V_k(3)=V_1(3)$ for every $k\geq1$. If $\varphi\in A_{g,1}(k)$ and $\psi\in B_{g,1}$ agree modulo $\Gamma_{k+1}$ on $\pi$, does some $\mu\in AB_{g,1}$ satisfy $\mu(x)=\varph... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195](https://doi.org/10.4171/owr/2016/56)
## Literature review (checked 2026-08-21)
**Status:** open
**As... | 3 | partially_solved | null | 2,016 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1016/0040-9383%2889%2990011-6",
"checked_at": "2026-09-30",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-09-30] **partially_solved**. W. Pitsch (OWR 56/2016, pp. 3171–3172) asks for a description of V_k(3) (Question 1), whether V_k(3) = V₁(3) for all k (Question 2), and a realization question (Question 3). Known to the source: k = 2 (Morita, [Topology 28 (1989)](https://doi.org/10.10... | [
"owr",
"oberwolfach-reports",
"OWR-15177-003",
"literature-status:open",
"owr-year:2016"
] | Johnson-filtration and mapping-class-group methods give partial information, but the asserted equality of the third-level images and the requested simultaneous realization remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2016/56",
"label": "Oberwolfach Report 56 (2017)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/56 | null | null | null | For the Johnson-filtration images $V_k(3)$ of stable Heegaard splittings of integral homology $3$-spheres, describe $V_k(3)$ and determine whether $V_k(3)=V_1(3)$ for every $k\geq1$. If $\varphi\in A_{g,1}(k)$ and $\psi\in B_{g,1}$ agree modulo $\Gamma_{k+1}$ on $\pi$, does some $\mu\in AB_{g,1}$ satisfy $\mu(x)=\varph... | For the Johnson-filtration images V_k(3) of stable Heegaard splittings of integral homology 3-spheres, describe V_k(3) and determine whether V_k(3)=V_1(3) for every k greater than or equal to 1; additionally, if phi in A_{g,1}(k) and psi in B_{g,1} agree modulo Gamma_{k+1} on pi, does some mu in AB_{g,1} also satisfy m... | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195 |
30,003,290 | OWR-15177-005 | Monodromy of Universal Plane-Curve Bundles | For the universal smooth plane-curve bundle of degree $d\geq4$, is the monodromy group $\Gamma_d$ equal to the stabilizer $\operatorname{Mod}_g[\phi_d]$ of the associated $(d-3)$-spin structure, where $g=(d-1)(d-2)/2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195](https://doi.org/10.4171/owr/2016/56)
## Literature review (checked 2026-08-21)
**Status:** open
**As... | 3 | solved | null | 2,016 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://doi.org/10.1007/s00222-018-0845-6",
"checked_at": "2026-10-02",
"kind": "resolution",
"evidence": "published"
} | null | null | null | [Discussion #4 literature review, 2026-10-02] **solved (yes)**. N. Salter (OWR 56/2016, p. 3181, Conjecture 6) conjectures that for every d ≥ 4 the monodromy group Γ\_d of the universal family of smooth plane curves of degree d equals the stabilizer Mod\_g[φ\_d] of its (d − 3)-spin structure; d = 4 is classical and d =... | [
"owr",
"oberwolfach-reports",
"OWR-15177-005",
"literature-status:open",
"owr-year:2016"
] | The report states the maximal-monodromy assertion as a conjecture for all relevant degrees, and no complete proof of that conjecture was found. | [
{
"url": "https://doi.org/10.4171/owr/2016/56",
"label": "Oberwolfach Report 56 (2017)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/56 | null | null | null | For the universal smooth plane-curve bundle of degree $d\geq4$, is the monodromy group $\Gamma_d$ equal to the stabilizer $\operatorname{Mod}_g[\phi_d]$ of the associated $(d-3)$-spin structure, where $g=(d-1)(d-2)/2$? | For the universal smooth plane-curve bundle of degree d greater than or equal to 4, is the monodromy group Gamma_d equal to the stabilizer Mod_g[phi_d] of the associated (d-3)-spin structure, where g=(d-1)(d-2)/2? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195 |
30,003,291 | OWR-15177-008 | Unbounded Simplicial Volume in Surface-Bundle Families | For the surface bundles $E_R$ over $\Sigma_2$ constructed with pullback simplicial volumes at least $R$, does the simplicial volume of $E_R$ tend to infinity as $R\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195](https://doi.org/10.4171/owr/2016/56)
## Literature review (checked 2026-08-21)
**Status:** open
**As... | 3 | open | null | 2,016 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15177-008",
"literature-status:open",
"owr-year:2016"
] | The extracted record does not define E sub R sufficiently to identify a theorem proving the stated limit; related surface-bundle constructions give unbounded examples but do not establish this exact assertion, so it is open under the triage rule. | [
{
"url": "https://doi.org/10.4171/owr/2016/56",
"label": "Oberwolfach Report 56 (2017)"
},
{
"url": "https://arxiv.org/abs/1605.03226",
"label": "Bucher and Campagnolo"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/56 | null | null | null | For the surface bundles $E_R$ over $\Sigma_2$ constructed with pullback simplicial volumes at least $R$, does the simplicial volume of $E_R$ tend to infinity as $R\to\infty$? | For the surface bundles E_R over Sigma_2 constructed with pullback simplicial volumes at least R, does the simplicial volume of E_R tend to infinity as R tends to infinity? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195 |
30,003,292 | OWR-15177-009 | Coherence and Finiteness Properties of Surface-Bundle Groups | Let $E$ be the total space of a bundle with closed-surface base $B$ and fiber $F$, and let $\pi=\pi_1(E)$. Is $\pi$ coherent? Does every finitely presented subgroup $G\leq\pi$ admit a finite $K(G,1)$? More generally, is every subgroup of type $\mathrm{FP}^{\lfloor n/2\rfloor}$ of a $\mathrm{PD}^n$ group necessarily of ... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195](https://doi.org/10.4171/owr/2016/56)
## Literature review (checked 2026-08-21)
**Status:** partially ... | 3 | partially_solved | null | 2,016 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15177-009",
"literature-status:partially-solved",
"owr-year:2016"
] | Coherence and finiteness properties are established in several cases and non-coherence is forced in others, but the full three-part question for arbitrary surface-by-surface groups remains open. | [
{
"url": "https://doi.org/10.4171/owr/2016/56",
"label": "Oberwolfach Report 56 (2017)"
},
{
"url": "https://people.maths.ox.ac.uk/~bridson/papers/BMiller07/BMiller08.pdf",
"label": "Baumslag and Roseblade subgroup theorem"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/56 | null | null | null | Let $E$ be the total space of a bundle with closed-surface base $B$ and fiber $F$, and let $\pi=\pi_1(E)$. Is $\pi$ coherent? Does every finitely presented subgroup $G\leq\pi$ admit a finite $K(G,1)$? More generally, is every subgroup of type $\mathrm{FP}^{\lfloor n/2\rfloor}$ of a $\mathrm{PD}^n$ group necessarily of ... | Let E be the total space of a bundle with closed surface base B and fibre F, and let pi=pi_1(E). Is pi coherent; does every finitely presented subgroup G of pi admit a finite K(G,1); and, more generally, is an FP^{floor(n/2)} subgroup of a PD^n group necessarily FP? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195 |
30,003,293 | OWR-15177-010 | Multiple Kodaira Fiberings and Relative Irregularity | Do compact complex surfaces exist with three or more Kodaira fiberings? Can one obtain better or asymptotically sharp upper bounds, as the fiber genus $g(F)$ grows, for the relative irregularity $q_f$ of a nonisotrivial fibered Kähler surface, especially a Kodaira fibration? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195](https://doi.org/10.4171/owr/2016/56)
## Literature review (checked 2026-08-21)
**Status:** open
**As... | 3 | open | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15177-010",
"literature-status:open",
"owr-year:2016"
] | Later work gives constraints on multiple Kodaira fibrations and many relative-irregularity bounds, but existence of three or more Kodaira fibrations and asymptotically sharp bounds remain unresolved. | [
{
"url": "https://arxiv.org/abs/2001.03694",
"label": "Llosa Isenrich and Py"
},
{
"url": "https://doi.org/10.4171/owr/2016/56",
"label": "Oberwolfach Report 56 (2017)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/56 | null | null | null | Do compact complex surfaces exist with three or more Kodaira fiberings? Can one obtain better or asymptotically sharp upper bounds, as the fiber genus $g(F)$ grows, for the relative irregularity $q_f$ of a nonisotrivial fibered Kähler surface, especially a Kodaira fibration? | Do complex compact surfaces exist with three or more Kodaira fiberings over surfaces; and can one obtain better or asymptotically sharp upper bounds, as the fibre genus g(F) grows, for the relative irregularity q_f of a non-isotrivial fibred Kahler complex surface, especially for a Kodaira fibration? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195 |
30,003,294 | OWR-15177-011 | Non-Liftable Monodromy of Surface Bundles | Does there exist a nonflat surface bundle $\Sigma_g\to E\to\Sigma_h$ for which the monodromy homomorphism from $\pi_1(\Sigma_h)$ to $\operatorname{Mod}_g$ does not lift through $\operatorname{Diff}^+(\Sigma_g)$ in the category of groups? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195](https://doi.org/10.4171/owr/2016/56)
## Literature review (checked 2026-08-21)
**Status:** open
**As... | 3 | open | null | 2,016 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15177-011",
"literature-status:open",
"owr-year:2016"
] | Baykur proves only the approximate statement that certain bundles admit no flat connection making a distinguished section parallel, while the bundles themselves are flat; the full closed-fiber lifting problem remains open. | [
{
"url": "https://arxiv.org/abs/1206.3512",
"label": "Baykur Flat bundles and commutator lengths"
},
{
"url": "https://doi.org/10.4171/owr/2016/56",
"label": "Oberwolfach Report 56 (2017)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/56 | null | null | null | Does there exist a nonflat surface bundle $\Sigma_g\to E\to\Sigma_h$ for which the monodromy homomorphism from $\pi_1(\Sigma_h)$ to $\operatorname{Mod}_g$ does not lift through $\operatorname{Diff}^+(\Sigma_g)$ in the category of groups? | Does there exist a non-flat surface bundle Sigma_g to E to Sigma_h over a surface for which the lifting problem from pi_1(Sigma_h) to Mod_g through Diff^+(F_g) cannot be solved in the category of groups? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195 |
30,003,295 | OWR-15177-012 | Asymptotic Point Counts on Curve Moduli Spaces | For fixed $q$, does the ratio of the number of $\mathbb F_q$-valued points of the coarse moduli space $\mathcal M_g$ to $q^{3g-3}$ have a finite positive limit as $g\to\infty$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195](https://doi.org/10.4171/owr/2016/56)
## Literature review (checked 2026-08-21)
**Status:** open
**As... | 3 | open | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15177-012",
"literature-status:open",
"owr-year:2016"
] | Point counts are computable in low genus and related cohomological data are known in ranges, but the positive finite limit for the normalized coarse-moduli count is not established; recent asymptotic discussions remain conjectural or heuristic. | [
{
"url": "https://doi.org/10.4171/owr/2016/56",
"label": "Oberwolfach Report 56 (2017)"
},
{
"url": "https://arxiv.org/abs/1409.6090",
"label": "van der Geer Counting curves over finite fields"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/56 | null | null | null | For fixed $q$, does the ratio of the number of $\mathbb F_q$-valued points of the coarse moduli space $\mathcal M_g$ to $q^{3g-3}$ have a finite positive limit as $g\to\infty$? | For fixed q, does the ratio of the number of F_q-valued points of the coarse moduli space M_g to q^{3g-3} have a finite positive limit as g tends to infinity? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195 |
30,003,296 | OWR-15177-013 | Complete Surfaces inside the Genus-Four Moduli Space | Does the moduli space $\mathcal M_4$ of smooth genus-$4$ curves contain a complete complex subvariety of complex dimension $2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195](https://doi.org/10.4171/owr/2016/56)
## Literature review (checked 2026-08-21)
**Status:** open
**As... | 3 | open | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15177-013",
"literature-status:open",
"owr-year:2016"
] | The Diaz and Looijenga bounds allow dimension 2 in M4, but the checked literature still gives no existence or nonexistence theorem for a complete complex surface. | [
{
"url": "https://doi.org/10.4171/owr/2016/56",
"label": "OWR 56 (2017)"
},
{
"url": "https://arxiv.org/abs/2404.06009",
"label": "Grushevsky--Mondello--Salvati Manni--Tsimerman, compact subvarieties"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/56 | null | null | null | Does the moduli space $\mathcal M_4$ of smooth genus-$4$ curves contain a complete complex subvariety of complex dimension $2$? | Does the moduli space M_4 of smooth genus-4 curves contain a complete complex subvariety of complex dimension 2? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195 |
30,003,297 | OWR-15177-015 | Boundedness of Tautological Kappa Classes | Are the tautological kappa classes on mapping class groups bounded cohomology classes? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195](https://doi.org/10.4171/owr/2016/56)
## Literature review (checked 2026-08-21)
**Status:** partially ... | 3 | partially_solved | null | 2,016 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15177-015",
"literature-status:partially-solved",
"owr-year:2016"
] | Odd kappa classes are bounded, while stable MMM polynomials are unbounded; the stated coefficient-cohomology and SL3 embedding questions remain unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2016/56",
"label": "OWR 56 (2017)"
},
{
"url": "https://arxiv.org/abs/2308.14171",
"label": "Kastenholz, bounded cohomology stability"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/56 | null | null | null | Are the tautological kappa classes on mapping class groups bounded cohomology classes? | Are the kappa classes bounded cohomology classes; for torsion-free finite-index Gamma contained in Mod_g, is H^{2g-1}(Gamma;H^{2g-2}(C_g)) infinitely generated; and does there exist a finite-volume hyperbolic 3-manifold M with an injective homomorphism pi_1(M) to SL_3(Z)? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195 |
30,003,298 | OWR-15177-016 | Infinite Generation in Mapping-Class-Group Cohomology | If $\Gamma$ is a torsion-free finite-index subgroup of $\operatorname{Mod}_g$ and $\mathcal C_g$ is the curve complex, is $H^{2g-1}(\Gamma;H_{2g-2}(\mathcal C_g))$ infinitely generated? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195](https://doi.org/10.4171/owr/2016/56)
## Literature review (checked 2026-08-21)
**Status:** open
**As... | 3 | open | null | 2,016 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15177-016",
"literature-status:open",
"owr-year:2016"
] | No checked primary source proves or disproves infinite generation of the stated mapping-class-group cohomology group. | [
{
"url": "https://doi.org/10.4171/owr/2016/56",
"label": "OWR 56 (2017)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/56 | null | null | null | If $\Gamma$ is a torsion-free finite-index subgroup of $\operatorname{Mod}_g$ and $\mathcal C_g$ is the curve complex, is $H^{2g-1}(\Gamma;H_{2g-2}(\mathcal C_g))$ infinitely generated? | If Gamma is a torsion-free finite-index subgroup of Mod_g and C_g is the universal curve, is H^{2g-1}(Gamma;H^{2g-2}(C_g)) infinitely generated? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195 |
30,003,299 | OWR-15177-017 | Hyperbolic Three-Manifold Groups in $\operatorname{SL}_3(\mathbb Z)$ | Does there exist a finite-volume hyperbolic $3$-manifold $M$ whose fundamental group admits an injective homomorphism $\pi_1(M)\to\operatorname{SL}_3(\mathbb Z)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195](https://doi.org/10.4171/owr/2016/56)
## Literature review (checked 2026-08-21)
**Status:** open
**As... | 3 | open | null | 2,016 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15177-017",
"literature-status:open",
"owr-year:2016"
] | The existence of a finite-volume hyperbolic 3-manifold group embedding in SL3(Z) is still posed as an open small-subgroups question; no example or obstruction was found. | [
{
"url": "https://doi.org/10.4171/owr/2016/56",
"label": "OWR 56 (2017)"
},
{
"url": "https://web.math.ucsb.edu/~long/pubpdf/smallsubgroups2.pdf",
"label": "Long--Reid--Thistlethwaite, small subgroups of SL3(Z)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/56 | null | null | null | Does there exist a finite-volume hyperbolic $3$-manifold $M$ whose fundamental group admits an injective homomorphism $\pi_1(M)\to\operatorname{SL}_3(\mathbb Z)$? | Does there exist a finite-volume hyperbolic 3-manifold M whose fundamental group admits an injective homomorphism \pi_1(M) \to SL_3(\mathbb{Z})? | corrected_verified | Checked against the official Oberwolfach report; the clean statement preserves the report's hypotheses, notation, and open mathematical target. | null | null | null | null | null | Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195 |
30,003,300 | OWR-15177-018 | Coherence and Free-Product Subgroups of $\operatorname{SL}_3(\mathbb Z)$ | Is $\operatorname{SL}_3(\mathbb Z)$ coherent, or does it contain a subgroup isomorphic to $(\mathbb Z\times\mathbb Z)*\mathbb Z$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195](https://doi.org/10.4171/owr/2016/56)
## Literature review (checked 2026-08-21)
**Status:** open
**As... | 3 | open | null | 2,016 | 17 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 17,
"name": "group_theory",
"display_name": "Group Theory",
"description": "Problems about groups, group actions, representations, and related algebraic structures.",
"slug": "group-theory",
"order_index": 17,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15177-018",
"literature-status:open",
"owr-year:2016"
] | The clipped record contains unresolved alternatives about SL3(Z), including Serre's coherence question; the checked literature still treats them as open. | [
{
"url": "https://doi.org/10.4171/owr/2016/56",
"label": "OWR 56 (2017)"
},
{
"url": "https://www.math.ucdavis.edu/~kapovich/EPR/ICERM-problems-2022-08-15.pdf",
"label": "ICERM problems on discrete subgroups"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/56 | null | null | null | Is $\operatorname{SL}_3(\mathbb Z)$ coherent, or does it contain a subgroup isomorphic to $(\mathbb Z\times\mathbb Z)*\mathbb Z$? | Is SL_3(\mathbb{Z}) coherent, or does SL_3(\mathbb{Z}) contain a subgroup isomorphic to (\mathbb{Z}\times\mathbb{Z})\ast\mathbb{Z}? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195 |
30,003,301 | OWR-15177-019 | Lifting Dehn-Twist Relations to Punctured Surfaces | Given a relation $t_{a_1}\cdots t_{a_n}=1$ of Dehn twists in $\operatorname{Mod}_g$, can the curves be moved away from the puncture to curves $\widetilde a_i$ in the punctured surface satisfying $t_{\widetilde a_1}\cdots t_{\widetilde a_n}=1$ in $\operatorname{Mod}_{g,1}$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195](https://doi.org/10.4171/owr/2016/56)
## Literature review (checked 2026-08-21)
**Status:** open
**As... | 3 | partially_solved | null | 2,016 | 7 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 7,
"name": "topology",
"display_name": "Topology",
"description": "Properties preserved under continuous deformations.",
"slug": "topology",
"order_index": 7,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | {
"source_url": "https://arxiv.org/abs/2610.01776",
"checked_at": "2026-10-02",
"kind": "partial",
"evidence": "unrefereed_claim"
} | null | null | null | [Discussion #4 literature review, 2026-10-02] **solved (no; unrefereed preprint)**. M. Korkmaz (OWR 56/2016, p. 3189, Question 13) asks whether the curves of every relation t\_{a₁}⋯t\_{aₙ} = 1 of Dehn twists in Mod\_g can be moved off the puncture so that t\_{ã₁}⋯t\_{ãₙ} = 1 in Mod\_{g,1}; for positive relations this a... | [
"owr",
"oberwolfach-reports",
"OWR-15177-019",
"literature-status:open",
"owr-year:2016"
] | No checked primary source gives a general theorem lifting every Dehn-twist relation from Modg to curves avoiding the puncture in Modg,1. | [
{
"url": "https://doi.org/10.4171/owr/2016/56",
"label": "OWR 56 (2017)"
},
{
"url": "https://arxiv.org/abs/math/9801025",
"label": "Gervais, a presentation of mapping class groups"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/56 | null | null | null | Given a relation $t_{a_1}\cdots t_{a_n}=1$ of Dehn twists in $\operatorname{Mod}_g$, can the curves be moved away from the puncture to curves $\widetilde a_i$ in the punctured surface satisfying $t_{\widetilde a_1}\cdots t_{\widetilde a_n}=1$ in $\operatorname{Mod}_{g,1}$? | Given a relation t_{a_1}\cdots t_{a_n}=1 of Dehn twists in Mod_{g}, can the curves be moved away from the puncture to curves \widetilde a_i in the punctured surface satisfying t_{\widetilde a_1}\cdots t_{\widetilde a_n}=1 in Mod_{g,1}? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195 |
30,003,302 | OWR-15177-020 | Convex Exhaustions of Curve Moduli Spaces | Does the moduli space $\mathcal M_g$ admit a proper, bounded-below, orbifold-smooth, $(g-2)$-convex function $f:\mathcal M_g\to\mathbb R$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195](https://doi.org/10.4171/owr/2016/56)
## Literature review (checked 2026-08-21)
**Status:** open
**As... | 3 | open | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15177-020",
"literature-status:open",
"owr-year:2016"
] | The requested proper bounded-below (g-2)-convex exhaustion of Mg remains an unverified strengthening of the known cohomological dimension bounds. | [
{
"url": "https://doi.org/10.4171/owr/2016/56",
"label": "OWR 56 (2017)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/56 | null | null | null | Does the moduli space $\mathcal M_g$ admit a proper, bounded-below, orbifold-smooth, $(g-2)$-convex function $f:\mathcal M_g\to\mathbb R$? | Does the moduli space M_g admit a proper, bounded-below, orbifold-smooth, (g-2)-convex function f:M_g\to\mathbb{R}? | corrected_verified | Manual semantic, typographic, and LaTeX review confirmed that the clean statement is self-contained and preserves the mathematical target without adding unsupported content. | null | null | null | null | null | Surface Bundles (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/56, pp. 3149--3195 |
30,003,303 | OWR-15178-003 | Lech Multiplicity Conjecture for Flat Local Extensions | Lech's conjecture: if $(R,\mathfrak m)\to(S,\mathfrak n)$ is a flat local extension of Noetherian local rings, then $e(R)\leq e(S)$. | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Asymptotic Phenomena in Local Algebra and Singularity Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/57, pp. 3199--3259](https://doi.org/10.4171/owr/2016/57)
## Literature review... | 3 | open | null | 2,016 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15178-003",
"literature-status:open",
"owr-year:2016"
] | Lech's inequality is known through dimension 3 in equal characteristic and in several special classes, but the general conjecture remains open, including higher dimensions. | [
{
"url": "https://doi.org/10.1016/j.aim.2017.10.032",
"label": "Ma, Lech's conjecture in dimension three"
},
{
"url": "https://arxiv.org/abs/2005.02338",
"label": "Ma, lim Ulrich sequences and Lech's conjecture"
},
{
"url": "https://doi.org/10.4171/owr/2016/57",
"label": "OWR 57 (201... | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/57 | null | null | null | Lech's conjecture: if $(R,\mathfrak m)\to(S,\mathfrak n)$ is a flat local extension of Noetherian local rings, then $e(R)\leq e(S)$. | Lech's conjecture: if (R,\mathfrak m)\to(S,\mathfrak n) is a flat local extension of Noetherian local rings, then e(R)\le e(S). | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Asymptotic Phenomena in Local Algebra and Singularity Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/57, pp. 3199--3259 |
30,003,304 | OWR-15178-011 | Embedded Resolution of Singularities in Positive Characteristic | Does embedded resolution of singularities exist in dimension three or higher, in the sense of resolving $X\subset Z$ by a sequence of blowups in regular centers while preserving the embedding? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Asymptotic Phenomena in Local Algebra and Singularity Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/57, pp. 3199--3259](https://doi.org/10.4171/owr/2016/57)
## Literature review... | 3 | open | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15178-011",
"literature-status:open",
"owr-year:2016"
] | The historical wording is too broad because characteristic-zero resolution is known, but general embedded resolution in positive characteristic beyond the known low-dimensional cases remains open. | [
{
"url": "https://arxiv.org/abs/1711.03453",
"label": "Hauser, singularities in positive characteristic"
},
{
"url": "https://doi.org/10.4171/owr/2016/57",
"label": "OWR 57 (2017)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/57 | null | null | null | Does embedded resolution of singularities exist in dimension three or higher, in the sense of resolving $X\subset Z$ by a sequence of blowups in regular centers while preserving the embedding? | Does embedded resolution of singularities exist in dimension three or higher, in the sense of resolving X\subset Z by a sequence of blowups in regular centers while preserving the embedding? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Asymptotic Phenomena in Local Algebra and Singularity Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/57, pp. 3199--3259 |
30,003,305 | OWR-15178-012 | Multiplicity Inequality for Quotients by Perfect Ideals | If $(T,\mathfrak n)$ is a local ring and $J\subset T$ is a perfect ideal, must the multiplicities satisfy $e(T)\leq e(T/J)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Asymptotic Phenomena in Local Algebra and Singularity Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/57, pp. 3199--3259](https://doi.org/10.4171/owr/2016/57)
## Literature review... | 3 | open | null | 2,016 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15178-012",
"literature-status:open",
"owr-year:2016"
] | The perfect-ideal inequality e(T) less than or equal to e(T/J) is a Lech-type strengthening known only in special cases and remains unresolved in general. | [
{
"url": "https://arxiv.org/abs/1609.00095",
"label": "Ma, Lech's conjecture in dimension three"
},
{
"url": "https://doi.org/10.4171/owr/2016/57",
"label": "OWR 57 (2017)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/57 | null | null | null | If $(T,\mathfrak n)$ is a local ring and $J\subset T$ is a perfect ideal, must the multiplicities satisfy $e(T)\leq e(T/J)$? | If (T,\mathfrak n) is a local ring and J\subset T is a perfect ideal, must the multiplicities satisfy e(T)\le e(T/J)? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Asymptotic Phenomena in Local Algebra and Singularity Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/57, pp. 3199--3259 |
30,003,306 | OWR-15178-013 | Toric Reembeddings for Embedded Local Uniformization | Given an affine variety $X\subset\mathbb{A}^n(k)$ without a prescribed embedded resolution, how can one construct suitable re-embeddings $X\subset\mathbb{A}^N(k)$ and toric maps that yield embedded local uniformizations? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Asymptotic Phenomena in Local Algebra and Singularity Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/57, pp. 3199--3259](https://doi.org/10.4171/owr/2016/57)
## Literature review... | 3 | open | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15178-013",
"literature-status:open",
"owr-year:2016"
] | No general construction of the proposed re-embeddings is known that replaces the missing embedded resolution in the stated setting. | [
{
"url": "https://arxiv.org/abs/1711.03453",
"label": "Hauser, singularities in positive characteristic"
},
{
"url": "https://doi.org/10.4171/owr/2016/57",
"label": "OWR 57 (2017)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/57 | null | null | null | Given an affine variety $X\subset\mathbb{A}^n(k)$ without a prescribed embedded resolution, how can one construct suitable re-embeddings $X\subset\mathbb{A}^N(k)$ and toric maps that yield embedded local uniformizations? | Given an affine variety X\subset\mathbb{A}^n(k) without a prescribed embedded resolution, how can one construct suitable re-embeddings X\subset\mathbb{A}^N(k) and toric maps that yield embedded local uniformizations? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Asymptotic Phenomena in Local Algebra and Singularity Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/57, pp. 3199--3259 |
30,003,307 | OWR-15178-015 | Multiplicity Reduction by Regular Equimultiple Blowups | Can reduction of the multiplicity of a variety in positive characteristic be proved by blowing up along regular equimultiple centers, in particular for $X=\operatorname{Spec}(B)\to W=\operatorname{Spec}(S)$ with $S\subset B$ purely inseparable and S regular? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Asymptotic Phenomena in Local Algebra and Singularity Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/57, pp. 3199--3259](https://doi.org/10.4171/owr/2016/57)
## Literature review... | 3 | open | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15178-015",
"literature-status:open",
"owr-year:2016"
] | Reduction of multiplicity by regular equimultiple blowups is a recognized route to positive-characteristic resolution, but the general reduction problem remains open. | [
{
"url": "https://arxiv.org/abs/1711.03453",
"label": "Hauser, singularities in positive characteristic"
},
{
"url": "https://doi.org/10.4171/owr/2016/57",
"label": "OWR 57 (2017)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/57 | null | null | null | Can reduction of the multiplicity of a variety in positive characteristic be proved by blowing up along regular equimultiple centers, in particular for $X=\operatorname{Spec}(B)\to W=\operatorname{Spec}(S)$ with $S\subset B$ purely inseparable and S regular? | Can reduction of the multiplicity of a variety in positive characteristic be proved by blowing up along regular equimultiple centers, in particular for X=\operatorname{Spec}(B)\to W=\operatorname{Spec}(S) with S\subset B purely inseparable and S regular? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Asymptotic Phenomena in Local Algebra and Singularity Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/57, pp. 3199--3259 |
30,003,308 | OWR-15178-016 | Gorenstein Monomial Curves from Principal Matrices | Can one characterize Gorenstein monomial curves in $\mathbb{A}^5$ defined by relatively prime positive integers $a_1,\ldots,a_5$ in terms of their principal matrix? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Asymptotic Phenomena in Local Algebra and Singularity Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/57, pp. 3199--3259](https://doi.org/10.4171/owr/2016/57)
## Literature review... | 3 | partially_solved | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15178-016",
"literature-status:partially-solved",
"owr-year:2016"
] | The report gives a principal-matrix criterion for decomposable length-five Gorenstein sequences, but the requested criterion for all length-five sequences is not established. | [
{
"url": "https://doi.org/10.4171/owr/2016/57",
"label": "OWR 57 (2017)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/57 | null | null | null | Can one characterize Gorenstein monomial curves in $\mathbb{A}^5$ defined by relatively prime positive integers $a_1,\ldots,a_5$ in terms of their principal matrix? | Can one characterize Gorenstein monomial curves in \mathbb{A}^5 defined by relatively prime positive integers a_1,\ldots,a_5 in terms of their principal matrix? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Asymptotic Phenomena in Local Algebra and Singularity Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/57, pp. 3199--3259 |
30,003,309 | OWR-15178-017 | Generator Bounds for Gorenstein Monomial Curve Ideals | Are the numbers of generators of the defining ideals of affine Gorenstein monomial curves in $\mathbb{A}^n$ bounded independently of n and the curve? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Asymptotic Phenomena in Local Algebra and Singularity Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/57, pp. 3199--3259](https://doi.org/10.4171/owr/2016/57)
## Literature review... | 3 | open | null | 2,016 | 5 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 5,
"name": "algebraic_geometry",
"display_name": "Algebraic Geometry",
"description": "Geometric objects defined by polynomial equations.",
"slug": "algebraic-geometry",
"order_index": 5,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15178-017",
"literature-status:open",
"owr-year:2016"
] | Known results give bounds or unbounded families in restricted settings, but the universal boundedness question for defining ideals of affine Gorenstein monomial curves remains open. | [
{
"url": "https://doi.org/10.1007/BF01303625",
"label": "Bresinsky, monomial Gorenstein ideals"
},
{
"url": "https://doi.org/10.4171/owr/2016/57",
"label": "OWR 57 (2017)"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/57 | null | null | null | Are the numbers of generators of the defining ideals of affine Gorenstein monomial curves in $\mathbb{A}^n$ bounded independently of n and the curve? | Are the numbers of generators of the defining ideals of affine Gorenstein monomial curves in \mathbb{A}^n bounded independently of n and the curve? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Asymptotic Phenomena in Local Algebra and Singularity Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/57, pp. 3199--3259 |
30,003,310 | OWR-15178-020 | Asymptotic Lengths of Local Cohomology Modules | Let $(R,\mathfrak m)$ be a d-dimensional local ring, I an ideal, and $(I_n)$ a decreasing sequence cofinal with the powers of I. If $\operatorname{length}H^i_{\mathfrak m}(R/I_n)<\infty$ for all sufficiently large n, what is the asymptotic behavior of $l_n^i=\operatorname{length}H^i_{\mathfrak m}(R/I_n)$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Asymptotic Phenomena in Local Algebra and Singularity Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/57, pp. 3199--3259](https://doi.org/10.4171/owr/2016/57)
## Literature review... | 3 | partially_solved | null | 2,016 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15178-020",
"literature-status:partially-solved",
"owr-year:2016"
] | Dao and Montaño proved asymptotic upper bounds and actual rational limits for important classes, including suitable monomial ideals, but the broad local-ring question in the record is not fully settled. | [
{
"url": "https://arxiv.org/abs/1705.05033",
"label": "Dao--Montaño"
},
{
"url": "https://doi.org/10.4171/owr/2016/57",
"label": "original OWR report"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/57 | null | null | null | Let $(R,\mathfrak m)$ be a d-dimensional local ring, I an ideal, and $(I_n)$ a decreasing sequence cofinal with the powers of I. If $\operatorname{length}H^i_{\mathfrak m}(R/I_n)<\infty$ for all sufficiently large n, what is the asymptotic behavior of $l_n^i=\operatorname{length}H^i_{\mathfrak m}(R/I_n)$? | Let (R,\mathfrak m) be a d-dimensional local ring, I an ideal, and (I_n) a decreasing sequence cofinal with the powers of I. If length H^i_{\mathfrak m}(R/I_n)<\infty for all sufficiently large n, what is the asymptotic behavior of l_n^i=length H^i_{\mathfrak m}(R/I_n)? | corrected_verified | Only safe notation, typography, and TeX-delimiter cleanup was applied; all hypotheses, quantifiers, and subquestions are preserved. | null | null | null | null | null | Asymptotic Phenomena in Local Algebra and Singularity Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/57, pp. 3199--3259 |
30,003,311 | OWR-15178-021 | Large Regularity Quadratic Ideals with Linear First Syzygies | Does there exist a family of quadratic ideals $I_m\subset K[x_1,\ldots,x_m]$ with linearly generated first syzygies and $\lim_{m\to\infty}\operatorname{reg}(S/I_m)/m>0$? Also, is there a constant $\lambda$ such that $\operatorname{reg}K[\Delta]\leq\lambda$ whenever $K[\Delta]$ is Cohen–Macaulay and satisfies $N_2$? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Asymptotic Phenomena in Local Algebra and Singularity Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/57, pp. 3199--3259](https://doi.org/10.4171/owr/2016/57)
## Literature review... | 3 | partially_solved | null | 2,016 | 4 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 4,
"name": "algebra",
"display_name": "Algebra",
"description": "Group theory, ring theory, field theory, and algebraic structures.",
"slug": "algebra",
"order_index": 4,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15178-021",
"literature-status:partially-solved",
"owr-year:2016"
] | The monomial-ideal analogue is solved in the negative by arbitrarily large regularity with linear syzygies, while the stated family question for arbitrary quadratic ideals is not settled by that result. | [
{
"url": "https://doi.org/10.1112/S0010437X18007728",
"label": "Constantinescu--Kahle--Varbaro"
},
{
"url": "https://doi.org/10.4171/owr/2016/57",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.1007/s13348-015-0141-3",
"label": "linear syzygies and regularity"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/57 | null | null | null | Does there exist a family of quadratic ideals $I_m\subset K[x_1,\ldots,x_m]$ with linearly generated first syzygies and $\lim_{m\to\infty}\operatorname{reg}(S/I_m)/m>0$? Also, is there a constant $\lambda$ such that $\operatorname{reg}K[\Delta]\leq\lambda$ whenever $K[\Delta]$ is Cohen–Macaulay and satisfies $N_2$? | Does there exist a family of quadratic ideals I_m\subset K[x_1,\ldots,x_m] with linearly generated first syzygies and lim_{m\to\infty}reg(S/I_m)/m>0? Also, is there a constant \lambda such that reg K[\Delta]\le\lambda whenever K[\Delta] is Cohen--Macaulay and satisfies N_2? | corrected_verified | Notation, typography, and sentence structure were repaired without changing the mathematical content. | null | null | null | null | null | Asymptotic Phenomena in Local Algebra and Singularity Theory (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/57, pp. 3199--3259 |
30,003,312 | OWR-15181-001 | Model Theory and Analysis of Surreal Exponential Fields | For the logarithmic-exponential series field $\mathbb{T}$ with derivation $\partial$ and exponential map, is $(\mathbb{T},\partial,\exp)$ elementarily equivalent to $(\mathbf{No},\partial,\exp)$, and can every Hardy field closed under exponentiation be embedded in it? Can sine and cosine be defined on $\mathbf{No}$, ca... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Surreal Numbers, Surreal Analysis, Hahn Fields and Derivations (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/60, pp. 3313--3372](https://doi.org/10.4171/owr/2016/60)
## ... | 3 | partially_solved | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15181-001",
"literature-status:partially-solved",
"owr-year:2016"
] | Later work proves the differential Hardy-field embedding into No, but the exponential-compatible embedding and the additional composition, trigonometric, p-adic, and model-theoretic questions remain unresolved. | [
{
"url": "https://doi.org/10.4171/jems/858",
"label": "Aschenbrenner--van den Dries--van der Hoeven"
},
{
"url": "https://doi.org/10.4171/owr/2016/60",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.4171/jems/769",
"label": "Berarducci--Mantova"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/60 | null | null | null | For the logarithmic-exponential series field $\mathbb{T}$ with derivation $\partial$ and exponential map, is $(\mathbb{T},\partial,\exp)$ elementarily equivalent to $(\mathbf{No},\partial,\exp)$, and can every Hardy field closed under exponentiation be embedded in it? Can sine and cosine be defined on $\mathbf{No}$, ca... | For the logarithmic-exponential series field T with derivation \partial and exponential map, is (T,\partial,\exp) elementarily equivalent to (No,\partial,\exp), and can every Hardy field closed under exp be embedded in (No,\partial,\exp)? Can one define sin and cos on No and an exponential map on No[i], and does (No,+,... | corrected_verified | The official report passage was checked and the statement was rewritten as a self-contained problem while preserving its mathematical content. | null | null | null | null | null | Mini-Workshop: Surreal Numbers, Surreal Analysis, Hahn Fields and Derivations (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/60, pp. 3313--3372 |
30,003,313 | OWR-15181-002 | Composition and Elementary Equivalence in Surreal Differential Fields | Can a satisfactory composition operator be defined on all of $\mathbf{No}$? Are the EL-series elementarily equivalent to the omega-series field as differential fields? Does every $\kappa$-computable function on the Cauchy completion of $\mathbf{No}_\kappa$ satisfy the intermediate value theorem? Is there a Kaplansky di... | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Surreal Numbers, Surreal Analysis, Hahn Fields and Derivations (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/60, pp. 3313--3372](https://doi.org/10.4171/owr/2016/60)
## ... | 3 | open | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15181-002",
"literature-status:open",
"owr-year:2016"
] | The record collects several open problems; composition on all of No and the listed elementary-equivalence and embedding questions have no complete published resolution as of the check date. | [
{
"url": "https://doi.org/10.4171/owr/2016/60",
"label": "original OWR report"
},
{
"url": "https://arxiv.org/abs/1703.01995",
"label": "transseries as surreal functions"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/60 | null | null | null | Can a satisfactory composition operator be defined on all of $\mathbf{No}$? Are the EL-series elementarily equivalent to the omega-series field as differential fields? Does every $\kappa$-computable function on the Cauchy completion of $\mathbf{No}_\kappa$ satisfy the intermediate value theorem? Is there a Kaplansky di... | Can one find a good composition operator on all of No; are the EL-series elementarily equivalent to the omega-series field as differential fields; does every \kappa-computable function on the Cauchy completion of No_\kappa satisfy the intermediate value theorem; is there a Kaplansky differential embedding theorem for \... | corrected_verified | The official report passage was checked and the statement was rewritten as a self-contained problem while preserving its mathematical content. | null | null | null | null | null | Mini-Workshop: Surreal Numbers, Surreal Analysis, Hahn Fields and Derivations (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/60, pp. 3313--3372 |
30,003,314 | OWR-15181-003 | Valuation and Simplicity Problems for the Surreal Numbers | Can the degree map on $\mathbf{No}$ be extended to a field valuation? Can $\mathbb{Q}\subset\mathbf{No}$ be characterized by sign sequences? Can the simplicity order be extended to functions, and is the surreal exponential the simplest homomorphism with the required properties? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Surreal Numbers, Surreal Analysis, Hahn Fields and Derivations (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/60, pp. 3313--3372](https://doi.org/10.4171/owr/2016/60)
## ... | 3 | open | null | 2,016 | 18 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 18,
"name": "logic",
"display_name": "Logic",
"description": "Problems in mathematical logic, model theory, proof theory, and finite model theory.",
"slug": "logic",
"order_index": 18,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15181-003",
"literature-status:open",
"owr-year:2016"
] | Some component questions have positive results, including existence of integer parts for real closed fields, but the combined requests concerning No, explicit constructions without choice, and the remaining operations are unresolved. | [
{
"url": "https://doi.org/10.4171/owr/2016/60",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.4115/jla.2021.13.3",
"label": "Carl--Krapp"
},
{
"url": "https://doi.org/10.2307/2275224",
"label": "Mourgues--Ressayre"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/60 | null | null | null | Can the degree map on $\mathbf{No}$ be extended to a field valuation? Can $\mathbb{Q}\subset\mathbf{No}$ be characterized by sign sequences? Can the simplicity order be extended to functions, and is the surreal exponential the simplest homomorphism with the required properties? | Can deg be extended to a field valuation; can one develop integration and measure theory on No beyond the semialgebraic and globally subanalytic categories; can Q\subset No be characterized by sign-sequences; can the simplicity order be extended to functions; is exp the simplest suitable homomorphism; and can one expli... | corrected_verified | The official report passage was checked and the statement was rewritten as a self-contained problem while preserving its mathematical content. | null | null | null | null | null | Mini-Workshop: Surreal Numbers, Surreal Analysis, Hahn Fields and Derivations (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/60, pp. 3313--3372 |
30,003,315 | OWR-15181-004 | Closure Properties of Logarithmic Hardy Fields | For the quasianalytic asymptotic field $F=\bigcup_k F_k$ built from Ilyashenko algebras, what closure properties does $F$ have beyond being a Hardy field and being closed under logarithmic composition? | Collected from Oberwolfach Reports, which document mathematical workshops and their open-problem discussions.
**Source report:** [Mini-Workshop: Surreal Numbers, Surreal Analysis, Hahn Fields and Derivations (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/60, pp. 3313--3372](https://doi.org/10.4171/owr/2016/60)
## ... | 3 | open | null | 2,016 | 8 | 15 | 0 | 0 | 2026-08-25T00:00:00 | 2026-09-16T12:06:53 | true | {
"id": 8,
"name": "analysis",
"display_name": "Analysis",
"description": "Limits, continuity, calculus, and function theory.",
"slug": "analysis",
"order_index": 8,
"created_at": "2026-07-31T15:26:25.671Z"
} | {
"id": 3,
"level": 3,
"name": "L3: Advanced",
"description": "Difficult problems requiring specialized knowledge and sophisticated techniques.",
"color_class": "text-yellow-600 bg-yellow-50 border-yellow-200"
} | {
"id": 15,
"name": "oberwolfach_reports_open_problems",
"display_name": "Oberwolfach Reports Open Problems",
"description": "Open and partially solved problems extracted from Oberwolfach Reports workshop discussions, with report provenance and dated literature assessments.",
"slug": "oberwolfach-reports-open... | null | null | null | null | null | null | [
"owr",
"oberwolfach-reports",
"OWR-15181-004",
"literature-status:open",
"owr-year:2016"
] | The construction proves closure under differentiation and log-composition, while the broader request for further closure properties of F remains open. | [
{
"url": "https://doi.org/10.4171/owr/2016/60",
"label": "original OWR report"
},
{
"url": "https://doi.org/10.4153/CJM-2016-048-x",
"label": "Speissegger"
}
] | 2026-08-21T00:00:00 | null | https://doi.org/10.4171/owr/2016/60 | null | null | null | For the quasianalytic asymptotic field $F=\bigcup_k F_k$ built from Ilyashenko algebras, what closure properties does $F$ have beyond being a Hardy field and being closed under logarithmic composition? | If F is the Hardy field of germs constructed in the report and closed under log-composition, what other closure properties does F have? | corrected_verified | The official report passage was checked and the statement was rewritten as a self-contained problem while preserving its mathematical content. | null | null | null | null | null | Mini-Workshop: Surreal Numbers, Surreal Analysis, Hahn Fields and Derivations (2017), Oberwolfach Reports, DOI 10.4171/owr/2016/60, pp. 3313--3372 |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.